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Relevant bibliographies by topics / Time-Scales calculus

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Academic literature on the topic 'Time-Scales calculus'

Author: Grafiati

Published: 25 May 2024

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Journal articles on the topic "Time-Scales calculus"

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Khan, A. R., F. Mehmood та M. A. Shaikh. "Обобщение неравенств Островского на временных шкалах". Владикавказский математический журнал 25, № 3 (2023): 98–110. http://dx.doi.org/10.46698/q4172-3323-1923-j.

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The idea of time scales calculus’ theory was initiated and introduced by Hilger (1988) in his PhD thesis order to unify discret and continuous analysis and to expend the discrete and continous theories to cases ``in between''. Since then, mathematical research in this field has exceeded more than 1000 publications and a lot of applications in the fields of science, i.e., operations research, economics, physics, engineering, statistics, finance and biology. Ostrowski proved an inequality to estimate the absolute deviation of a differentiable function from its integral mean. This result was obta

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Torrest, Delfim F. M. "The variational calculus on time scales." International Journal for Simulation and Multidisciplinary Design Optimization 4, no. 1 (2010): 11–25. http://dx.doi.org/10.1051/ijsmdo/2010003.

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Yaslan, İsmail. "Beta-Fractional Calculus on Time Scales." Journal of Fractional Calculus and Nonlinear Systems 4, no. 2 (2023): 48–60. http://dx.doi.org/10.48185/jfcns.v4i2.877.

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Sahir, Muhammad Jibril Shahab. "Uniformity of dynamic inequalities constituted on time Scales." Engineering and Applied Science Letters 3, no. 4 (2020): 19–27. http://dx.doi.org/10.30538/psrp-easl2020.0048.

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In this article, we present extensions of some well-known inequalities such as Young's inequality and Qi's inequality on fractional calculus of time scales. To find generalizations of such types of dynamic inequalities, we apply the time scale Riemann-Liouville type fractional integrals. We investigate dynamic inequalities on delta calculus and their symmetric nabla results. The theory of time scales is utilized to combine versions in one comprehensive form. The calculus of time scales unifies and extends some continuous forms and their discrete and quantum inequalities. By applying the calcul

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Malinowska, Agnieszka B., and Natália Martins. "The Second Noether Theorem on Time Scales." Abstract and Applied Analysis 2013 (2013): 1–14. http://dx.doi.org/10.1155/2013/675127.

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We extend the second Noether theorem to variational problems on time scales. As corollaries we obtain the classical second Noether theorem, the second Noether theorem for theh-calculus and the second Noether theorem for theq-calculus.

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Sahir, Muhammad Jibril Shahab. "Coordination of Classical and Dynamic Inequalities Complying on Time Scales." European Journal of Mathematical Analysis 3 (February 3, 2023): 12. http://dx.doi.org/10.28924/ada/ma.3.12.

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In this research article, we present extensions of some classical inequalities such as Schweitzer, Pólya–Szegö, Kantorovich and Greub–Rheinboldt inequalities of fractional calculus on time scales. To investigate generalizations of such types of classical inequalities, we use the time scales Riemann–Liouville type fractional integrals. We explore dynamic inequalities on delta calculus and their symmetric nabla versions. A time scale is an arbitrary nonempty closed subset of the real numbers. The theory of time scales is applied to combine results in one comprehensive form. The calculus of time

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Ganie, Javid Ahmad, and Renu Jain. "THE SUMUDU TRANSFORM ON DISCRETE TIME SCALES." Jnanabha 51, no. 02 (2021): 58–67. http://dx.doi.org/10.58250/jnanabha.2021.51208.

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The study of dynamic equations on time scale is an area of mathematics that has recently received a lot of attention. This type of calculus has been created in order to unify the study of discrete and continuous analysis. Integral transforms play a crucial role in analysis in solving differential and difference equations. In this paper, we introduce the Sumudu transform on two different time scales by using the theory of time scale calculus. Finally, we employ these definitions to derive the results like, convolution, delay(shift) and inversion on these discrete time scales. Further, these res

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Sahir, M. J. S. "Объединение классических и динамических неравенств, возникающих при анализе временных масштабов". Вестник КРАУНЦ. Физико-математические науки, № 4 (29 грудня 2020): 26–36. http://dx.doi.org/10.26117/2079-6641-2020-33-4-26-36.

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In this paper, we present an extension of dynamic Renyi’s inequality on time scales by using the time scale Riemann–Liouville type fractional integral. Furthermore, we find generalizations of the well–known Lyapunov’s inequality and Radon’s inequality on time scales by using the time scale Riemann–Liouville type fractional integrals. Our investigations unify and extend some continuous inequalities and their corresponding discrete analogues. В этой статье мы представляем расширение динамического неравенства Реньи на шкалы времени с помощью дробного интеграла типа Римана-Лиувилля. Кроме того, мы

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Zhao, Dafang, and Tongxing Li. "On conformable delta fractional calculus on time scales." Journal of Mathematics and Computer Science 16, no. 03 (2016): 324–35. http://dx.doi.org/10.22436/jmcs.016.03.03.

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Seiffertt, John. "Adaptive Resonance Theory in the time scales calculus." Neural Networks 120 (December 2019): 32–39. http://dx.doi.org/10.1016/j.neunet.2019.08.010.

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Dissertations / Theses on the topic "Time-Scales calculus"

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Ferreira, Rui Alexandre Cardoso. "Calculus of variations on time scales and discrete fractional calculus." Doctoral thesis, Universidade de Aveiro, 2010. http://hdl.handle.net/10773/2921.

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Doutoramento em Matemática<br>Estudamos problemas do cálculo das variações e controlo óptimo no contexto das escalas temporais. Especificamente, obtemos condições necessárias de optimalidade do tipo de Euler–Lagrange tanto para lagrangianos dependendo de derivadas delta de ordem superior como para problemas isoperimétricos. Desenvolvemos também alguns métodos directos que permitem resolver determinadas classes de problemas variacionais através de desigualdades em escalas temporais. No último capítulo apresentamos operadores de diferença fraccionários e propomos um novo cálculo das variações fr

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Dryl, Monika. "Calculus of variations on time scales and applications to economics." Doctoral thesis, Universidade de Aveiro, 2014. http://hdl.handle.net/10773/12869.

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Doutoramento em Matemática<br>We consider some problems of the calculus of variations on time scales. On the beginning our attention is paid on two inverse extremal problems on arbitrary time scales. Firstly, using the Euler-Lagrange equation and the strengthened Legendre condition, we derive a general form for a variation functional that attains a local minimum at a given point of the vector space. Furthermore, we prove a necessary condition for a dynamic integro-differential equation to be an Euler-Lagrange equation. New and interesting results for the discrete and quantum calculus ar

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Bastos, Nuno Rafael de Oliveira. "Fractional calculus on time scales - Cálculo fraccional em escalas temporais." Doctoral thesis, Universidade de Aveiro, 2012. http://hdl.handle.net/10773/8566.

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Doutoramento em Matemática<br>Introduzimos um cálculo das variações fraccional nas escalas temporais ℤ e (hℤ)!. Estabelecemos a primeira e a segunda condição necessária de optimalidade. São dados alguns exemplos numéricos que ilustram o uso quer da nova condição de Euler–Lagrange quer da nova condição do tipo de Legendre. Introduzimos também novas definições de derivada fraccional e de integral fraccional numa escala temporal com recurso à transformada inversa generalizada de Laplace.<br>We introduce a discrete-time fractional calculus of variations on the time scales ℤ and (ℎℤ)!. First a

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McMahon, Chris. "Calculus of Variations on Time Scales and Its Applications to Economics." TopSCHOLAR®, 2008. http://digitalcommons.wku.edu/theses/370.

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The goal of time scale research is to progress the development of a harmonized theory that is all encompassing of the more commonly known specialized forms. The main results of this paper is the presentation of the Ramsey model which can be written using both the A and V operators, and solved using the two separate theories of the calculus of variations on time scales. The next presentation will be of the solution of an adjustment model, for a specific form of a time scale, whose functional can only be optimized, using the existing theory, when written with the A operator. We will also develop

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Hariz, Belgacem Khader. "Higher-order Embedding Formalism, Noether’s Theorem on Time Scales and Eringen’s Nonlocal Elastica." Electronic Thesis or Diss., Pau, 2022. https://theses.hal.science/tel-03981833.

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En mathématiques, le calcul des variations est un ensemble de méthodes permettant la détermination de solutions à des problèmes d'optimisation des quantités traduites en termes de fonctionnelle. De nombreuses applications existent, notamment dans la recherche de courbes ou de surfaces minimales. Les systèmes dynamiques considérés sont de natures diverses (équations différentielles, intégrales ou stochastiques) et modélisent des problèmes d'origines multiples : aérospatiale, automobile, biologie, économie, médecine, etc. Le théorème de Noether présente un fort intérêt puisqu'il propose une loi

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Arslan, Aykut. "Discrete Fractional Hermite-Hadamard Inequality." TopSCHOLAR®, 2017. http://digitalcommons.wku.edu/theses/1940.

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This thesis is comprised of three main parts: The Hermite-Hadamard inequality on discrete time scales, the fractional Hermite-Hadamard inequality, and Karush-Kuhn- Tucker conditions on higher dimensional discrete domains. In the first part of the thesis, Chapters 2 & 3, we define a convex function on a special time scale T where all the time points are not uniformly distributed on a time line. With the use of the substitution rules of integration we prove the Hermite-Hadamard inequality for convex functions defined on T. In the fourth chapter, we introduce fractional order Hermite-Hadamard ine

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Kisela, Tomáš. "Basics of Qualitative Theory of Linear Fractional Difference Equations." Doctoral thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2012. http://www.nusl.cz/ntk/nusl-234025.

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Tato doktorská práce se zabývá zlomkovým kalkulem na diskrétních množinách, přesněji v rámci takzvaného (q,h)-kalkulu a jeho speciálního případu h-kalkulu. Nejprve jsou položeny základy teorie lineárních zlomkových diferenčních rovnic v (q,h)-kalkulu. Jsou diskutovány některé jejich základní vlastnosti, jako např. existence, jednoznačnost a struktura řešení, a je zavedena diskrétní analogie Mittag-Lefflerovy funkce jako vlastní funkce operátoru zlomkové diference. Dále je v rámci h-kalkulu provedena kvalitativní analýza skalární a vektorové testovací zlomkové diferenční rovnice. Výsledky analý

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Books on the topic "Time-Scales calculus"

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Bohner, Martin, and Svetlin G. Georgiev. Multivariable Dynamic Calculus on Time Scales. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-47620-9.

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Georgiev, Svetlin G. Fractional Dynamic Calculus and Fractional Dynamic Equations on Time Scales. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-73954-0.

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Variational Calculus on Time Scales. Nova Science Publishers, Incorporated, 2018.

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Georgiev, Svetlin G. Variational Calculus on Time Scales. Nova Science Publishers, Incorporated, 2018.

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Bohner, Martin, and Svetlin G. Georgiev. Multivariable Dynamic Calculus on Time Scales. Springer, 2017.

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Bohner, Martin, and Svetlin G. Georgiev. Multivariable Dynamic Calculus on Time Scales. Springer, 2017.

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Bohner, Martin, and Svetlin G. Georgiev. Multivariable Dynamic Calculus on Time Scales. Springer, 2018.

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Hardy Type Inequalities on Time Scales. Springer, 2016.

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O'Regan, Donal, Ravi P. Agarwal, and Samir H. Saker. Hardy Type Inequalities on Time Scales. Springer, 2016.

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O'Regan, Donal, Ravi P. Agarwal, and Samir H. Saker. Hardy Type Inequalities on Time Scales. Springer, 2018.

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Book chapters on the topic "Time-Scales calculus"

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Bohner, Martin, and Svetlin G. Georgiev. "Time Scales." In Multivariable Dynamic Calculus on Time Scales. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-47620-9_1.

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Seiffertt, John, and Donald C. Wunsch. "The Time Scales Calculus." In Evolutionary Learning and Optimization. Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-03180-9_4.

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Georgiev, Svetlin G. "Calculus on Time Scales." In Functional Dynamic Equations on Time Scales. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-15420-2_1.

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Bohner, Martin, and Allan Peterson. "The Time Scales Calculus." In Dynamic Equations on Time Scales. Birkhäuser Boston, 2001. http://dx.doi.org/10.1007/978-1-4612-0201-1_1.

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Goodrich, Christopher, and Allan C. Peterson. "Calculus on Mixed Time Scales." In Discrete Fractional Calculus. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-25562-0_5.

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Georgiev, Svetlin G. "Elements of the Time Scale Calculus." In Integral Equations on Time Scales. Atlantis Press, 2016. http://dx.doi.org/10.2991/978-94-6239-228-1_1.

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Bohner, Martin, and Svetlin G. Georgiev. "Partial Differentiation on Time Scales." In Multivariable Dynamic Calculus on Time Scales. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-47620-9_6.

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Bohner, Martin, and Svetlin G. Georgiev. "Multiple Integration on Time Scales." In Multivariable Dynamic Calculus on Time Scales. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-47620-9_7.

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Bohner, Martin, Gusein Guseinov, and Allan Peterson. "Introduction to the Time Scales Calculus." In Advances in Dynamic Equations on Time Scales. Birkhäuser Boston, 2003. http://dx.doi.org/10.1007/978-0-8176-8230-9_1.

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Georgiev, Svetlin G. "Convolution on Time Scales." In Fractional Dynamic Calculus and Fractional Dynamic Equations on Time Scales. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-73954-0_3.

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Conference papers on the topic "Time-Scales calculus"

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Kapcak, Sinan, and Ünal Ufuktepe. "Multivariable Calculus on Time Scales." In 2011 International Conference on Computational Science and Its Applications (ICCSA). IEEE, 2011. http://dx.doi.org/10.1109/iccsa.2011.28.

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Girejko, Ewa, Agnieszka B. Malinowska, and Delfim F. M. Torres. "A unified approach to the calculus of variations on time scales." In 2010 Chinese Control and Decision Conference (CCDC). IEEE, 2010. http://dx.doi.org/10.1109/ccdc.2010.5498972.

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Niu, Haoyu, YangQuan Chen, Lihong Guo, and Bruce J. West. "A New Triangle: Fractional Calculus, Renormalization Group, and Machine Learning." In ASME 2021 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2021. http://dx.doi.org/10.1115/detc2021-70505.

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Abstract The emergence of the systematic study of complexity as a science has resulted from the growing recognition that the fundamental assumptions upon which Newtonian physics is based are not satisfied throughout most of science, e.g., time is not necessarily uniformly flowing in one direction, nor is space homogeneous. Herein we discuss how the fractional calculus (FC), renormalization group (RG) theory and machine learning (ML) have each developed independently in the study of distinct phenomena in which one or more of the underlying assumptions of Newtonian formalism is violated. FC has

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