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Journal articles on the topic 'Derivative'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Gaudinskaitė, Danguolė. "Lietuvių kalbos sinonimiškų bendrašaknių asmenų pavadinimų darybos kategorijos." Vārds un tā pētīšanas aspekti: rakstu krājums = The Word: Aspects of Research: conference proceedings, no. 24 (December 2, 2020): 64–78. http://dx.doi.org/10.37384/vtpa.2020.24.064.

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In the Lithuanian language, persons are named by simple words and formations. The latter are divided into the categories of derivation according to their derivational meaning. The categories of derivation involve synonymous formations, i.e., derivative synonyms, and some formations are coherent in variance relation (they are derivative variants). The article aims to analyse the categories of derivation of synonymous conjugate personal names. The methods of derivational and semantic analysis, as well as calculation, were applied in the present research. The article discusses 1179 nominal person

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2

Tsamparlis, Michael. "Derivation of Tensor Algebra as a Fundamental Operation—The Fermi Derivative in a General Metric Affine Space." Symmetry 17, no. 1 (2025): 81. https://doi.org/10.3390/sym17010081.

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The aim of this work is to demonstrate that all linear derivatives of the tensor algebra over a smooth manifold M can be viewed as specific cases of a broader concept—the operation of derivation. This approach reveals the universal role of differentiation, which simplifies and generalizes the study of tensor derivatives, making it a powerful tool in Differential Geometry and related fields. To perform this, the generic derivative is introduced, which is defined in terms of the quantities Qk(i)(X). Subsequently, the transformation law of these quantities is determined by the requirement that th

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3

Rehman, Hameed Ur, Maslina Darus, and Jamal Salah. "A Note on Caputo’s Derivative Operator Interpretation in Economy." Journal of Applied Mathematics 2018 (October 1, 2018): 1–7. http://dx.doi.org/10.1155/2018/1260240.

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We propound the economic idea in terms of fractional derivatives, which involves the modified Caputo’s fractional derivative operator. The suggested economic interpretation is based on a generalization of average count and marginal value of economic indicators. We use the concepts ofT-indicatorswhich analyses the economic performance with the presence of memory. The reaction of economic agents due to recurrence identical alteration is minimized by using the modified Caputo’s derivative operator of orderλinstead of integer order derivativen. The two sides of Caputo’s derivative are expressed by

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4

Farid, Ghulam, and Zeeshan Afzal. "Further on quantum-plank derivatives and integrals in composite forms." Open Journal of Mathematical Analysis 6, no. 2 (2022): 130–38. http://dx.doi.org/10.30538/psrp-oma2022.0118.

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In quantum-plank calculus, q-derivatives and h-derivatives are fundamental factors. Recently, a composite form of both derivatives is introduced and called q−h-derivative. This paper aims to present a further generalized notion of derivatives will be called (q ,p−h)-derivatives. This will produce q-derivative, h-derivative, q−h-derivative and (p,q)-derivative. Theory based on all aforementioned derivatives can be generalized via this new notion. It is expected, this paper will be useful and beneficial for researchers working in diverse fields of sciences and engineering.

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5

Gao, Zhe. "A Tuning Method via Borges Derivative of a Neural Network-Based Discrete-Time Fractional-Order PID Controller with Hausdorff Difference and Hausdorff Sum." Fractal and Fractional 5, no. 1 (2021): 23. http://dx.doi.org/10.3390/fractalfract5010023.

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In this paper, the fractal derivative is introduced into a neural network-based discrete-time fractional-order PID controller in two areas, namely, in the controller’s structure and in the parameter optimization algorithm. The first use of the fractal derivative is to reconstruct the fractional-order PID controller by using the Hausdorff difference and Hausdorff sum derived from the Hausdorff derivative and Hausdorff integral. It can avoid the derivation of the Gamma function for the order updating to realize the parameter and order tuning based on neural networks. The other use is the optimiz

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6

Gaudinskaitė, Danguolė. "Derivative Synonyms (Derivative Variants) of the Names of Persons Possessing Nominal Characteristics." Acta humanitarica academiae Saulensis 27 (April 3, 2025): 126–47. https://doi.org/10.15388/ahas.2020.9.

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In the Lithuanian language, the persons can be named by synonymous words (simple words and derivatives). A variety is revealed by lexical, derivative, syntactical synonyms as well as other language means. Derivative synonyms, which are one of the type of synonyms, are such derivatives of the Lithuanian language that have the same root, the same derivative meaning, but which are formed with different derivative means. Derivative variants should be distinguished from derivative synonyms: they are the derivatives formed from the same underlying word (or from the same underlying words) with the sa

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7

Shapiro, Ilya L. "Covariant Derivative of Fermions and All That." Universe 8, no. 11 (2022): 586. http://dx.doi.org/10.3390/universe8110586.

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We present detailed pedagogical derivation of covariant derivative of fermions and some related expressions, including commutator of covariant derivatives and energy-momentum tensor of a free Dirac field. On top of that, local conformal transformations for a Dirac fermion in curved spacetime are considered and we obtain the expression for the energy-momentum tensor on the cosmological background.

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8

Popov, Igor. "Scalar and vector division and derivatives vectors." Applied Mathematics and Control Sciences, no. 2 (June 29, 2018): 43–55. http://dx.doi.org/10.15593/2499-9873/2018.2.03.

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The work is devoted to the operations of differentiation in the space of vector fields and smooth functions. In mechanics, it is widely used derivative of a scalar function of the vector. To some extent, like it is determined by the derivative of the vector to another vector. However, formally interpreting the derivative as division differentials are entered in consideration of scalar and vector derived vector on another vector, which may have application to the solution of problems of mechanics. The definition of a derivative of a scalar vector field on another vector field. We prove a theore

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9

Lazopoulos, Anastasios K., and Dimitrios Karaoulanis. "Fractional Derivatives and Projectile Motion." Axioms 10, no. 4 (2021): 297. http://dx.doi.org/10.3390/axioms10040297.

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Projectile motion is studied using fractional calculus. Specifically, a newly defined fractional derivative (the Leibniz L-derivative) and its successor (Λ-fractional derivative) are used to describe the motion of the projectile. Experimental data were analyzed in this study, and conclusions were made. The results of well-established fractional derivatives were also compared with those of L-derivative and Λ-fractional derivative, showing the many advantages of these new derivatives.

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10

Gaudinskaitė, Danguolė. "Sinonimiški bendrašakniai asmenų pagal profesiją pavadinimai: daryba, semantika, stilistika ir vartosena." Acta humanitarica academiae Saulensis 28 (December 30, 2021): 8–28. http://dx.doi.org/10.15388/ahas.2021.1.

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The nominal names of persons belong to different categories of formation (for example, the names of persons possessing nominal features, the names of persons by profession, etc.). A total of 1,266 conjugate synonymous nominal derivatives (or possessing one of the components of nominal words) naming the persons by profession were collected from the Dictionary of Lithuanian Language and its electronic version, out of them 386 rows of derivative synonyms (derivative variants) were formed. The derivatives were analysed in terms of formation, semantics, stylistics and usage. To achieve the aim, the

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11

Tseng, Yuan-Wei, and Jer-Guang Hsieh. "Optimal Control for a Family of Systems in Novel State Derivative Space Form with Experiment in a Double Inverted Pendulum System." Abstract and Applied Analysis 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/715026.

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Optimal control for a family of systems in novel state derivative space form, abbreviated as SDS systems in this study, is proposed. The first step in deriving optimal control laws for SDS systems is to form an augmented cost functional. It turns out that novel differential Lagrange multipliers must be used to adjoin SDS system constraints (namely, the dynamical equations of the control system) to the integrand of the original cost functional which is a function of state derivatives. This not only eases our derivation but also makes our derivation parallel to that for systems in standard state

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12

TARASOV, VASILY E. "FRACTIONAL DERIVATIVE AS FRACTIONAL POWER OF DERIVATIVE." International Journal of Mathematics 18, no. 03 (2007): 281–99. http://dx.doi.org/10.1142/s0129167x07004102.

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Definitions of fractional derivatives as fractional powers of derivative operators are suggested. The Taylor series and Fourier series are used to define fractional power of selfadjoint derivative operator. The Fourier integrals and Weyl quantization procedure are applied to derive the definition of fractional derivative operator. Fractional generalization of concept of stability is considered.

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13

Bedair, A. H., Abd El-Wahab, A. M. El-Agrody, F. M. Ali, A. H. Halawa, and G. M. El-Sherbiny. "Binary heterocyclic systems containing the ethylideneamino linkage: synthesis of some new heterocyclic compounds bearing the naphtho-[2,1-b]furan moiety." Journal of the Serbian Chemical Society 71, no. 5 (2006): 459–69. http://dx.doi.org/10.2298/jsc0605459b.

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Ethylidene hydrazine (4a,b) and thiazolidin-4-one (5) derivatives were synthesized by the reaction of ethylidenethiosemicarbazide derivative (3a) with ?-haloketone/ethyl bromoacetate, respectively. Hetrocyclization of ethylideneacetohydrazide derivative (7) with o-phenolic aldehydes gave the corresponding coumarin derivatives (8,9). The interaction of 7 with acetylacetone afforded the corresponding pyridine derivative (10). Treatment of the arylidene derivative 11b with malononitrile afforded the corresponding pyran derivative (12). The new products 3-12 were subjected to IR, 1H NMR and mass s

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14

Farayola, Musiliu Folarin, Sharidan Shafie, Fuaada Mohd Siam, Rozi Mahmud, and Suraju Olusegun Ajadi. "Mathematical modeling of cancer treatments with fractional derivatives: An Overview." Malaysian Journal of Fundamental and Applied Sciences 17, no. 4 (2021): 389–401. http://dx.doi.org/10.11113/mjfas.v17n4.2062.

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This review article presents fractional derivative cancer treatment models to show the importance of fractional derivatives in modeling cancer treatments. Cancer treatment is a significant research area with many mathematical models developed by mathematicians to represent the cancer treatment processes like hyperthermia, immunotherapy, chemotherapy, and radiotherapy. However, many of these models were based on ordinary derivatives and the use of fractional derivatives is still new to many mathematicians. Therefore, it is imperative to review fractional cancer treatment models. The review was

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15

Deppman, Airton, Eugenio Megías, and Roman Pasechnik. "Fractal Derivatives, Fractional Derivatives and q-Deformed Calculus." Entropy 25, no. 7 (2023): 1008. http://dx.doi.org/10.3390/e25071008.

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This work presents an analysis of fractional derivatives and fractal derivatives, discussing their differences and similarities. The fractal derivative is closely connected to Haussdorff’s concepts of fractional dimension geometry. The paper distinguishes between the derivative of a function on a fractal domain and the derivative of a fractal function, where the image is a fractal space. Different continuous approximations for the fractal derivative are discussed, and it is shown that the q-calculus derivative is a continuous approximation of the fractal derivative of a fractal function. A sim

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16

Plitzner, Patrick, Andreas Müller, Anton Güntsch, et al. "The CDM Applied: Unit-Derivation, from Field Observations to DNA Sequences." Biodiversity Information Science and Standards 1 (August 16, 2017): e20366. https://doi.org/10.3897/tdwgproceedings.1.20366.

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Specimens form the falsifiable evidence used in plant systematics. Derivatives of specimens (including the specimen as the organism in the field) such as tissue and DNA samples play an increasing role in research. The EDIT Platform for Cybertaxonomy is a specialist's tool that allows to document and sustainably store all data that are used in the taxonomic work process, from field data to DNA sequences. The types of data stored can be very heterogeneous consisting of specimens, images, text data, primary data files, taxon assignments, etc. The EDIT Platform organizes the linking between such d

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17

Easton, CJ, and SC Peters. "Synthesis of Novel Cross-Linked Amino Acid Derivatives." Australian Journal of Chemistry 43, no. 1 (1990): 87. http://dx.doi.org/10.1071/ch9900087.

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Reactions of the derivatives of cysteine (6), serine (7) and lysine (8a), with the bromide (1), afforded the corresponding cross-linked amino acid derivatives (11), (12) and (13). Of the linked species (11)-(13), the cysteine derivative (11) was found to be the most stable under a variety of conditions. A mixture of the cross-linked serine derivative (12) and the cysteine derivative (6) in chloroform containing triethylamine reacted to give the cross-linked cysteine derivative (11) and the serine derivative (7). Similarly, a mixture of (13) and (6) in chloroform reacted to give (11).

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18

Moloi, Tankiso. "The nature of the derivative market transactions traded in the Johannesburg securities exchange." Risk Governance and Control: Financial Markets and Institutions 4, no. 3 (2014): 90–101. http://dx.doi.org/10.22495/rgcv4i3c1art3.

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The main objective of the study was to assess and understand the nature of derivative products traded in the Johannesburg Securities Exchange (JSE) by analysing daily transactions consisting of deals and contracts concluded, as well as notional values of derivatives traded in the review period. Analysed data found that the South African derivative market continues to grow and evolve with the consistent introduction of new derivative products such as the “can do” derivatives, IDX derivatives that are now being traded at the JSE. The evolvement and growth is confirmed by the fact that the total

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19

Emmons, Brad, and Xiao Xiao. "A generalization of arithmetic derivative to p-adic fields and number fields." Notes on Number Theory and Discrete Mathematics 30, no. 2 (2024): 357–82. http://dx.doi.org/10.7546/nntdm.2024.30.2.357-382.

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The arithmetic derivative is a function from the natural numbers to itself that sends all prime numbers to 1 and satisfies the Leibniz rule. The arithmetic partial derivative with respect to a prime p is the p-th component of the arithmetic derivative. In this paper, we generalize the arithmetic partial derivative to p-adic fields (the local case) and the arithmetic derivative to number fields (the global case). We study the dynamical system of the p-adic valuation of the iterations of the arithmetic partial derivatives. We also prove that for every integer n \geq 0, there are infinitely many

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20

Shi, Da, Ghulam Farid, Bakri Adam Ibrahim Younis, Hanaa Abu-Zinadah, and Matloob Anwar. "A Unified Representation of q- and h-Integrals and Consequences in Inequalities." Axioms 13, no. 4 (2024): 278. http://dx.doi.org/10.3390/axioms13040278.

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This paper aims to unify q-derivative/q-integrals and h-derivative/h-integrals into a single definition, called q−h-derivative/q−h-integral. These notions are further extended on the finite interval [a,b] in the form of left and right q−h-derivatives and q−h-integrals. Some inequalities for q−h-integrals are studied and directly connected with well known results in diverse fields of science and engineering. The theory based on q-derivatives/q-integrals and h-derivatives/h-integrals can be unified using the q−h-derivative/q−h-integral concept.

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21

Cai, Min, and Changpin Li. "On Riesz derivative." Fractional Calculus and Applied Analysis 22, no. 2 (2019): 287–301. http://dx.doi.org/10.1515/fca-2019-0019.

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Abstract This paper focuses on studying Riesz derivative. An interesting investigation on properties of Riesz derivative in one dimension indicates that it is distinct from other fractional derivatives such as Riemann-Liouville derivative and Caputo derivative. In the existing literatures, Riesz derivative is commonly considered as a proxy for fractional Laplacian on ℝ. We show the equivalence between Riesz derivative and fractional Laplacian on ℝn with n ≥ 1 in details.

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22

Burgess, VA, та CJ Easton. "Reaction of N-Benzoyl-2-bromoglycine Methyl Ester With Deprotonated Nitroalkanes: Synthesis of β-Nitro and α,β-Dehydro Amino Acid Derivatives". Australian Journal of Chemistry 41, № 7 (1988): 1063. http://dx.doi.org/10.1071/ch9881063.

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N-Benzoyl-2-bromoglycine methyl ester (1) reacted with the alkyl nitronates (2a-e) to give the corresponding β-nitro amino acid derivatives (4a-e). Elimination reactions of (4a-d) afforded the α,β-dehydro amino acid derivatives (5a-d). Treatment of the β- nitrovaline derivative (4b) with tributyltin hydride gave the valine derivative (8). Reduction of the β- nitroalanine derivative (4a) gave the β- aminoalanine derivative (9), characterized by hydrolysis to 2,3- diaminopropionic acid hydrochloride.

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23

Hasanah, Dahliatul. "On continuity properties of the improved conformable fractional derivatives." Jurnal Fourier 11, no. 2 (2022): 88–96. http://dx.doi.org/10.14421/fourier.2022.112.88-96.

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The conformable fractional derivative has been introduced to extend the familiar limit definition of the classical derivative. Despite having many advantages compared to other fractional derivatives such as satisfying nice properties as classical derivative and easy to solve numerically, it also has disadvantages as it gives large error compared to Riemann-Liouville and Caputo fractional derivatives. Modified types of conformable derivatives have been proposed to overcome the shortcoming. The improved conformal fractional derivatives are declared to be better approximations of Riemann-Liouvill

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24

Khurshaid*, Adil, and Hajra Khurshaid. "Comparative Analysis and Definitions of Fractional Derivatives." Journal of Biomedical Research & Environmental Sciences 4, no. 12 (2023): 1684–88. http://dx.doi.org/10.37871/jbres1852.

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Fractional Calculus (FC) has emerged as a valuable tool in various fields. This study explores the historical development of (FC) and examines prominent definitions regarding Fractional Derivatives (FD), such as the Riemann-Liouville, Grunwald-Letnikov, Caputo Fractional Derivative, Katugampula derivatives, Caputo Fractional Derivative, Caputo-Fabrizio Fractional Derivative and as well as Atangana-Baleanu Fractional Derivative. It critically evaluates their strengths, weaknesses and implications on (FD) equations. The findings contribute to establishing a clearer understanding of Fractional De

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25

Zuhdi, Muhammad, Bakti Sukrisna, and Syamsuddin Syamsuddin. "IDENTIFICATION OF BURIED ARCHEOLOGICAL OBJECTS WITH RADIAL DERIVATIVES OF MICRO GRAVITY DATA." Indonesian Physical Review 2, no. 2 (2019): 84. http://dx.doi.org/10.29303/ipr.v2i2.25.

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The development of recent gravimetric technology allows us to measure gravity anomalies with accuracy of micro Gal. Micro gravity is able to detect very small gravity anomalies such as anomaly due to buried archeological objects below the earth surface. Radial Derivatives of gravity data is used to sharpen anomaly due to lateral changes of density contrast. Horizontal derivatives carried out by previous researchers have some weaknesses, i.e. the loss of derivative values in certain directions and inconsistence values at the source boundary of the same anomaly edge. To solve the horizontal deri

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26

İlhan, Esin, and İ. Onur Kıymaz. "A generalization of truncated M-fractional derivative and applications to fractional differential equations." Applied Mathematics and Nonlinear Sciences 5, no. 1 (2020): 171–88. http://dx.doi.org/10.2478/amns.2020.1.00016.

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AbstractIn this paper, our aim is to generalize the truncated M-fractional derivative which was recently introduced [Sousa and de Oliveira, A new truncated M-fractional derivative type unifying some fractional derivative types with classical properties, Inter. of Jour. Analy. and Appl., 16 (1), 83–96, 2018]. To do that, we used generalized M-series, which has a more general form than Mittag-Leffler and hypergeometric functions. We called this generalization as truncated ℳ-series fractional derivative. This new derivative generalizes several fractional derivatives and satisfies important proper

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27

ETINKAYA, F. C. "A REVIEW ON THE EVOLUTION OF THE CONFORMABLE DERIVATIVE." Functional Differential Equations 29, no. 1 (2022): 23–37. http://dx.doi.org/10.26351/fde/29/1-2/2.

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This review paper focuses on the evolution of the conformable derivative. The review starts with expressing the idea behind the first research on the so-called conformable fractional derivative and examining some recent related papers. Then it continues mentioning some opposing papers which argue that the so-called conformable fractional derivative is actually not a fractional derivative because it lacks some of the agreed upon properties for fractional derivatives. The paper is closed by discussing another point of view on the theory of conformable derivatives.

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28

Galindo Illanes, Maritza Katherine, and Adriana Breda. "Processo de instrução do derivado aplicado a estudantes de engenharia de negócios no Chile." Uniciencia 38, no. 1 (2024): 1–23. http://dx.doi.org/10.15359/ru.38-1.17.

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[Objective] The objective of this article is to present the results of the implementation of an instructional design for the teaching of the derivative for undergraduate students of Business Engineering in Chile. [Methodology] The participants in the study were ninety students of Applied Business Calculus at a Chilean university. The methodological design, based on the tools of the Ontosemiotic Approach to Mathematical Cognition and Instruction, consider various epistemic configurations in situations-problems concerning tangents, the calculation of derivatives from the rules for derivation, ap

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29

Parmikanti, Kankan, and Endang Rusyaman. "Grundwald-Letnikov Operator and Its Role in Solving Fractional Differential Equations." EKSAKTA: Berkala Ilmiah Bidang MIPA 23, no. 03 (2022): 223–30. http://dx.doi.org/10.24036/eksakta/vol23-iss03/331.

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Leibnitz in 1663 introduced the derivative notation for the order of natural numbers, and then the idea of fractional derivatives appeared. Only a century later, this idea began to be realized with the discovery of the concepts of fractional derivatives by several mathematicians, including Riemann (1832), Grundwal, Fourier, and Caputo in 1969. The concepts in the definitions of fractional derivatives by Riemann-Liouville and Caputo are more frequently used than other definitions, this paper will discuss the Grunwald-Letnikov (GL) operator, which has been discovered in 1867. This concept is les

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30

Holman, Glen, Carlos Correia, Lucian Pitt, and Akios Majoni. "The corporate use of derivatives by listed non-financial firms in Africa." Corporate Ownership and Control 11, no. 1 (2013): 671–90. http://dx.doi.org/10.22495/cocv11i1c7art5.

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This paper presents the results of an extensive analysis of derivative use by 692 companies in 20 countries across the African continent. The results show that 29% of non-financial companies in Africa use derivatives but that derivative use is dominated by firms within South Africa. The study finds that 54% of firms in South Africa use derivatives but only 5% of non-financial firms in Africa (excluding South Africa) use derivatives for hedging purposes. The majority of derivative use is directed toward the management of currency risks and the derivative instrument of choice is OTC forwards. Sw

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Durur, Hülya, Ali Kurt, and Orkun Tasbozan. "New Travelling Wave Solutions for KdV6 Equation Using Sub Equation Method." Applied Mathematics and Nonlinear Sciences 5, no. 1 (2020): 455–60. http://dx.doi.org/10.2478/amns.2020.1.00043.

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AbstractThis paper proposes obtaining the new wave solutions of time fractional sixth order nonlinear Equation (KdV6) using sub-equation method where the fractional derivatives are considered in conformable sense. Conformable derivative is an understandable and applicable type of fractional derivative that satisfies almost all the basic properties of Newtonian classical derivative such as Leibniz rule, chain rule and etc. Also conformable derivative has some superiority over other popular fractional derivatives such as Caputo and Riemann-Liouville. In this paper all the computations are carrie

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Bayeğ, Selami, and Raziye Mert. "Generalized Hukuhara diamond-alpha derivative of fuzzy valued functions on time scales." Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics 74, no. 1 (2024): 103–16. https://doi.org/10.31801/cfsuasmas.1577063.

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In the literature, the delta and nabla derivatives have been considered separately in the study of fuzzy number valued functions on time scales. In this paper, to unify these two derivatives for fuzzy number valued functions, we propose a new dynamic derivative called the diamond-alpha derivative, defined via the generalized Hukuhara difference. We establish several fundamental properties of the diamond-alpha derivative and investigate a particular class of fuzzy initial value problems on time scales with respect to this new derivative. Additionally, we provide numerical examples to illustrate

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33

Novak, Oksana, Tetiana Osadcha, and Oleksandr Petruk. "CONCEPT AND CLASSIFICATION OF DERIVATIVE FINANCIAL INSTRUMENTS AS A METHODOLOGICAL PRECISION ON THEIR REGULATION IN THE FINANCIAL SERVICES MARKET." Baltic Journal of Economic Studies 5, no. 3 (2019): 135. http://dx.doi.org/10.30525/2256-0742/2019-5-3-135-144.

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The urgency of the research topic is caused by the rapid growth of capital markets and the emergence of all new financial instruments, the complexity of their structure and the transition beyond the regulatory influence of supervisory authorities. Discussion issues on the identification of derivatives, as well as their certain types, create significant problems with their valuation, the correctness of accounting, and the application of regulatory measures. Inconsistency in the interpretation of derivative financial instruments nature and their certain types is also present in domestic legal ac

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34

Solovyov, Leonid A. "Full-profile refinement by derivative difference minimization." Journal of Applied Crystallography 37, no. 5 (2004): 743–49. http://dx.doi.org/10.1107/s0021889804015638.

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A new method of full-profile refinement is developed on the basis of the minimization of the derivatives of the profile difference curve. The use of the derivatives instead of the absolute difference between the observed and calculated profile intensities allows refinement independently of the background. The procedure is tested on various powder diffraction data sets and is shown to be fully functional. Besides having the capability of powder diffraction structure analysis without modelling the background curve, the method is shown to allow the derivation of structure parameters of even highe

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35

Kaya, U. "CAUCHY FRACTIONAL DERIVATIVE." Bulletin of the South Ural State University series "Mathematics. Mechanics. Physics" 12, no. 4 (2020): 28–32. http://dx.doi.org/10.14529/mmph200403.

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In this paper, we introduce a new sort of fractional derivative. For this, we consider the Cauchy's integral formula for derivatives and modify it by using Laplace transform. So, we obtain the fractional derivative formula F(α)(s) = L{(–1)(α)L–1{F(s)}}. Also, we find a relation between Weyl's fractional derivative and the formula above. Finally, we give some examples for fractional derivative of some elementary functions.

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Peng, Zhenhua, and Zhongping Wan. "Second-Order Composed Contingent Derivative of the Perturbation Map in Multiobjective Optimization." Asia-Pacific Journal of Operational Research 37, no. 02 (2020): 2050002. http://dx.doi.org/10.1142/s0217595920500025.

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In view of the structural advantage of second-order composed derivatives, the purpose of this paper is to analyze quantitatively the behavior of perturbation maps for the first time by using this concept. First, new concepts of the second-order composed adjacent derivative and the second-order composed lower Dini derivative are introduced. Some relationships among the second-order composed contingent derivative, the second-order composed adjacent derivative and the second-order composed lower Dini derivative are discussed. Second, the relationships between second-order composed lower Dini deri

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37

Smetona, Antanas. "Regarding the Verb “ĮTAKOTI”." Lietuvių kalba, no. 16 (December 30, 2021): 98–110. http://dx.doi.org/10.15388/lk.2021.5.

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The first attempts to correct the verb įtakoti and, naturally, its derivatives were observed in the 1970s. The main assumption for correcting (not to mention a certain “tradition” of correcting) is as follows: įtaka – an inflectional derivative from įtekėti, therefore suffixal derivatives with -oti are not possible from the systemic perspective. Thus, this is the influence of the Russian language. However, such an assumption is erroneous and originates from misinterpretation of derivation and history of correcting. The article aims to show that, on the one hand, įtaka → įtakoti can be seen as

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Diethelm, Kai, Roberto Garrappa, Andrea Giusti, and Martin Stynes. "Why fractional derivatives with nonsingular kernels should not be used." Fractional Calculus and Applied Analysis 23, no. 3 (2020): 610–34. http://dx.doi.org/10.1515/fca-2020-0032.

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AbstractIn recent years, many papers discuss the theory and applications of new fractional-order derivatives that are constructed by replacing the singular kernel of the Caputo or Riemann-Liouville derivative by a non-singular (i.e., bounded) kernel. It will be shown here, through rigorous mathematical reasoning, that these non-singular kernel derivatives suffer from several drawbacks which should forbid their use. They fail to satisfy the fundamental theorem of fractional calculus since they do not admit the existence of a corresponding convolution integral of which the derivative is the left

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SUZUKI, MASUO. "GENERAL FORMULATION OF QUANTUM ANALYSIS." Reviews in Mathematical Physics 11, no. 02 (1999): 243–65. http://dx.doi.org/10.1142/s0129055x9900009x.

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A general formulation of noncommutative or quantum derivatives for operators in a Banach space is given on the basis of the Leibniz rule, irrespective of their explicit representations such as the Gâteaux derivative or commutators. This yields a unified formulation of quantum analysis, namely the invariance of quantum derivatives, which are expressed by multiple integrals of ordinary higher derivatives with hyperoperator variables. Multivariate quantum analysis is also formulated in the present unified scheme by introducing a partial inner derivation and a rearrangement formula. Operator Taylo

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Hattaf, Khalid. "On Some Properties of the New Generalized Fractional Derivative with Non-Singular Kernel." Mathematical Problems in Engineering 2021 (May 27, 2021): 1–6. http://dx.doi.org/10.1155/2021/1580396.

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This paper presents some new formulas and properties of the generalized fractional derivative with non-singular kernel that covers various types of fractional derivatives such as the Caputo–Fabrizio fractional derivative, the Atangana–Baleanu fractional derivative, and the weighted Atangana–Baleanu fractional derivative. These new properties extend many recent results existing in the literature. Furthermore, the paper proposes some interesting inequalities that estimate the generalized fractional derivatives of some specific functions. These inequalities can be used to construct Lyapunov funct

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Rajratana Maroti Kamble and Pramod Ramakant Kulkarni. "Extended fractional derivative: Some results involving classical properties and applications." Scientific Temper 15, no. 04 (2024): 3026–33. https://doi.org/10.58414/scientifictemper.2024.15.4.09.

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In this paper, considering the classical definition of derivative in the limit form, we can define a new fractional derivative called the extended fractional derivative, which depends upon two parameters α and a. For this new fractional derivative, we have proved the properties of classical derivatives such as the product rule, the quotient rule, the chain rule, Rolle’s and Lagrange’s mean value theorems, etc., which are nor satisfied by the existing fractional derivatives defined by Riemann Liouville, Caputo, Grunwald. Moreover, we have defined the extended fractional integral and proved some

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Hattaf, Khalid. "A New Mixed Fractional Derivative with Applications in Computational Biology." Computation 12, no. 1 (2024): 7. http://dx.doi.org/10.3390/computation12010007.

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This study develops a new definition of a fractional derivative that mixes the definitions of fractional derivatives with singular and non-singular kernels. This developed definition encompasses many types of fractional derivatives, such as the Riemann–Liouville and Caputo fractional derivatives for singular kernel types, as well as the Caputo–Fabrizio, the Atangana–Baleanu, and the generalized Hattaf fractional derivatives for non-singular kernel types. The associate fractional integral of the new mixed fractional derivative is rigorously introduced. Furthermore, a novel numerical scheme is d

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Babenko, V. F., and M. S. Churilova. "On inequalities of Kolmogorov type for fractional derivatives of functions defined on the real domain." Researches in Mathematics 16 (February 7, 2021): 28. http://dx.doi.org/10.15421/240804.

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We obtain new inequalities that generalize known result of Geisberg, which was obtained for fractional Marchaud derivatives, to the case of higher derivatives, at that the fractional derivative is a Riesz one. The inequality with second higher derivative is sharp.

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Manjushree, S. "A Derivative is a Risk Hedging Tool from Investor Perspective." Shanlax International Journal of Commerce 8, no. 3 (2020): 39–44. http://dx.doi.org/10.34293/commerce.v8i3.3131.

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Derivatives products provide certain important economic benefits such as risk management or redistribution of risk away from risk-averse investors towards those more willing and able to bear the risk. Derivatives also help price discovery, i.e., the process of determining the price level for any asset based on supply and demand. These functions of derivatives help inefficient capital allocation in the economy; at the same time, their misuse also poses a threat to the stability of the financial sector and the overall economy. In the mid-1990s, India started reviving the exchangetraded commodity

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Fedorov, Vladimir E., Marina V. Plekhanova, and Elizaveta M. Izhberdeeva. "Initial Value Problems of Linear Equations with the Dzhrbashyan–Nersesyan Derivative in Banach Spaces." Symmetry 13, no. 6 (2021): 1058. http://dx.doi.org/10.3390/sym13061058.

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Among the many different definitions of the fractional derivative, the Riemann–Liouville and Gerasimov–Caputo derivatives are most commonly used. In this paper, we consider the equations with the Dzhrbashyan–Nersesyan fractional derivative, which generalizes the Riemann–Liouville and the Gerasimov–Caputo derivatives; it is transformed into such derivatives for two sets of parameters that are, in a certain sense, symmetric. The issues of the unique solvability of initial value problems for some classes of linear inhomogeneous equations of general form with the fractional Dzhrbashyan–Nersesyan d

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Doungmo Goufo, Emile Franc, and Sunil Kumar. "Shallow Water Wave Models with and without Singular Kernel: Existence, Uniqueness, and Similarities." Mathematical Problems in Engineering 2017 (2017): 1–9. http://dx.doi.org/10.1155/2017/4609834.

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After the recent introduction of the Caputo-Fabrizio derivative by authors of the same names, the question was raised about an eventual comparison with the old version, namely, the Caputo derivative. Unlike Caputo derivative, the newly introduced Caputo-Fabrizio derivative has no singular kernel and the concern was about the real impact of this nonsingularity on real life nonlinear phenomena like those found in shallow water waves. In this paper, a nonlinear Sawada-Kotera equation, suitable in describing the behavior of shallow water waves, is comprehensively analyzed with both types of deriva

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Guswanto, Bambang Hendriya, Leony Rhesmafiski Andini, and Triyani Triyani. "On Conformable, Riemann-Liouville, and Caputo fractional derivatives." Bulletin of Applied Mathematics and Mathematics Education 2, no. 2 (2022): 59–64. http://dx.doi.org/10.12928/bamme.v2i2.7072.

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This article compares conformable fractional Derivative with Riemann-Liouville and Caputo fractional derivative by comparing solutions to fractional ordinary differential equations involving the three fractional derivatives via the numerical simulations of the solutions. The result shows that conformable fractional derivative can be used as an alternative to Riemann-Liouville and Caputo fractional derivative for order α with 1/2<α<1.

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Journal, Baghdad Science. "Synthesis and Characterization of New Heterocyclic Compounds from 2, 5- dimercapto -1, 3, 4-Thiadiazole and Their Resins." Baghdad Science Journal 13, no. 2 (2016): 275–88. http://dx.doi.org/10.21123/bsj.13.2.275-288.

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In this research, a new 1, 3, 4-Thiadiazole derivatives have been synthesized by many heterocyclic reactions. Starting from (2, 5 – dimercapto -1, 3, 4-Thiadiazole) a variety of derivatives have been synthesis. Compound (1) was synthesized by the reaction of hydrazine hydrate with carbon disulphide in absolute ethanol. The compound (1) was reacted with 1, 2-dibromoethane in presence of alkali ethanol to give the compound (2). The compound (3) was formed from the reaction of compound (2) with hydrazine hydrate. Schiff base (4) was obtained by reacting of compound (3) with the compound (p-hydrox

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Özkan, Ozan, and Ali Kurt. "Exact solutions of fractional partial differential equation systems with conformable derivative." Filomat 33, no. 5 (2019): 1313–22. http://dx.doi.org/10.2298/fil1905313o.

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Main goal of this paper is to have the new exact solutions of some fractional partial differential equation systems (FPDES) in conformable sense. The definition of conformable fractional derivative (CFD) is similar to the limit based definition of known derivative. This derivative obeys both rules which other popular derivatives do not satisfy such as derivative of the quotient of two functions, the derivative product of two functions, chain rule and etc. By using conformable derivative it is seen that the solution procedure for (PDES) is simpler and more efficient.

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Smith, Mark R. "Basic Derivatives for the Oil and Gas Company." Alberta Law Review 39, no. 1 (2001): 152. http://dx.doi.org/10.29173/alr511.

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This article provides a general overview of some of the basic derivatives available to oil and gas companies. The author begins by defining what a derivative is and briefly summarizing four basic kinds derive, of derivatives. The author offers other examples of derivative products and illustrates how oil and gas companies can design and utilize these products to meet their individual needs. The article includes a discussion of the 1SDA master agreement, which is used for most over-the-counter derivative contracts. As well, the article outlines some of the key regulatory provisions governing an

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