Thematische Bibliographien / Caputo derivatives

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Auswahl der wissenschaftlichen Literatur zum Thema „Caputo derivatives“

Autor: Grafiati

Veröffentlicht am 28. Juni 2021

Zuletzt aktualisiert am 6. Februar 2022

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Zeitschriftenartikel zum Thema "Caputo derivatives"

Li, Changpin, Deliang Qian und YangQuan Chen. „On Riemann-Liouville and Caputo Derivatives“. Discrete Dynamics in Nature and Society 2011 (2011): 1–15. http://dx.doi.org/10.1155/2011/562494.

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Recently, many models are formulated in terms of fractional derivatives, such as in control processing, viscoelasticity, signal processing, and anomalous diffusion. In the present paper, we further study the important properties of the Riemann-Liouville (RL) derivative, one of mostly used fractional derivatives. Some important properties of the Caputo derivative which have not been discussed elsewhere are simultaneously mentioned. The partial fractional derivatives are also introduced. These discussions are beneficial in understanding fractional calculus and modeling fractional equations in science and engineering.

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Oliveira, Daniela S., und Edmundo Capelas de Oliveira. „On a Caputo-type fractional derivative“. Advances in Pure and Applied Mathematics 10, Nr. 2 (01.04.2019): 81–91. http://dx.doi.org/10.1515/apam-2017-0068.

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Abstract In this paper, we present a new differential operator of arbitrary order defined by means of a Caputo-type modification of the generalized fractional derivative recently proposed by Katugampola. The generalized fractional derivative, when convenient limits are considered, recovers the Riemann–Liouville and the Hadamard derivatives of arbitrary order. Our differential operator recovers as limiting cases the arbitrary order derivatives proposed by Caputo and by Caputo–Hadamard. Some properties are presented as well as the relation between this differential operator of arbitrary order and the Katugampola generalized fractional operator. As an application we prove the fundamental theorem of fractional calculus associated with our operator.

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Rosales García, J. Juan, J. David Filoteo und Andrés González. „A comparative analysis of the RC circuit with local and non-local fractional derivatives“. Revista Mexicana de Física 64, Nr. 6 (31.10.2018): 647. http://dx.doi.org/10.31349/revmexfis.64.647.

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This work is devoted to investigate solutions to RC circuits using four different types of time fractional diferential operators of order 0 < γ ≤ 1. The fractional derivatives considered are, Caputo, Caputo-Fabrizio, Atangana-Baleanu and the conformable derivative. It is shown that Atangana-Baleanu fractional derivative (non-local), and the conformable (local) derivative could describe a wider class of physical processes then the Caputo and Caputo-Fabrizio. The solutions are exactly equal for all four erivatives only for the case γ=1.

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Diethelm, Kai, Roberto Garrappa, Andrea Giusti und Martin Stynes. „Why fractional derivatives with nonsingular kernels should not be used“. Fractional Calculus and Applied Analysis 23, Nr. 3 (25.06.2020): 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-inverse; and the value of the derivative at the initial time t = 0 is always zero, which imposes an unnatural restriction on the differential equations and models where these derivatives can be used. For the particular cases of the so-called Caputo-Fabrizio and Atangana-Baleanu derivatives, it is shown that when this restriction holds the derivative can be simply expressed in terms of integer derivatives and standard Caputo fractional derivatives, thus demonstrating that these derivatives contain nothing new.

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Baleanu, Dumitru, Bahram Agheli und Maysaa Mohamed Al Qurashi. „Fractional advection differential equation within Caputo and Caputo–Fabrizio derivatives“. Advances in Mechanical Engineering 8, Nr. 12 (Dezember 2016): 168781401668330. http://dx.doi.org/10.1177/1687814016683305.

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In this research, we applied the variational homotopic perturbation method and q-homotopic analysis method to find a solution of the advection partial differential equation featuring time-fractional Caputo derivative and time-fractional Caputo–Fabrizio derivative. A detailed comparison of the obtained results was reported. All computations were done using Mathematica.

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Feng, Xue, Baolin Feng, Ghulam Farid, Sidra Bibi, Qi Xiaoyan und Ze Wu. „Caputo Fractional Derivative Hadamard Inequalities for Stronglym-Convex Functions“. Journal of Function Spaces 2021 (21.04.2021): 1–11. http://dx.doi.org/10.1155/2021/6642655.

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In this paper, two versions of the Hadamard inequality are obtained by using Caputo fractional derivatives and stronglym-convex functions. The established results will provide refinements of well-known Caputo fractional derivative Hadamard inequalities form-convex and convex functions. Also, error estimations of Caputo fractional derivative Hadamard inequalities are proved and show that these are better than error estimations already existing in literature.

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Doungmo Goufo, Emile Franc, und 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 derivative. In the investigations, various fixed-point theories are exploited together with the concept of Piccard K-stability. We are then able to obtain the existence and uniqueness results for the models with both versions of derivatives. We conclude the analysis by performing some numerical approximations with both derivatives and graphical simulations being presented for some values of the derivative order γ. Similar behaviors are pointed out and they concur with the expected multisoliton solutions well known for the Sawada-Kotera equation. This great observation means either of both derivatives is suitable to describe the motion of shallow water waves.

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Abboubakar, Hamadjam, Pushpendra Kumar, Vedat Suat Erturk und Anoop Kumar. „A mathematical study of a tuberculosis model with fractional derivatives“. International Journal of Modeling, Simulation, and Scientific Computing 12, Nr. 04 (26.03.2021): 2150037. http://dx.doi.org/10.1142/s1793962321500379.

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In this work, we use a Predictor–Corrector method to implement and derive an iterative solution of an existing Tuberculosis (TB) model with two fractional derivatives, namely, Caputo–Fabrizio fractional derivative and the new generalized Caputo fractional derivative. We begin by recalling some existing results such as the basic reproduction number [Formula: see text] and the equilibrium points of the model. Then, we study the global asymptotic stability of disease-free equilibrium of the fractional models. We also prove, for each fractional model, the existence and uniqueness of solutions. An iterative solution of the two models is computed using the Predictor–Corrector method. Using realistic parameter values, we perform numerical simulations for different values of the fractional order. Simulation results permit to conclude that the new generalized Caputo fractional derivative provides a more realistic analysis than the Caputo–Fabrizio fractional derivative and the classical integer-order TB model.

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Khalighi, Moein, Leila Eftekhari, Soleiman Hosseinpour und Leo Lahti. „Three-Species Lotka-Volterra Model with Respect to Caputo and Caputo-Fabrizio Fractional Operators“. Symmetry 13, Nr. 3 (25.02.2021): 368. http://dx.doi.org/10.3390/sym13030368.

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In this paper, we apply the concept of fractional calculus to study three-dimensional Lotka-Volterra differential equations. We incorporate the Caputo-Fabrizio fractional derivative into this model and investigate the existence of a solution. We discuss the uniqueness of the solution and determine under what conditions the model offers a unique solution. We prove the stability of the nonlinear model and analyse the properties, considering the non-singular kernel of the Caputo-Fabrizio operator. We compare the stability conditions of this system with respect to the Caputo-Fabrizio operator and the Caputo fractional derivative. In addition, we derive a new numerical method based on the Adams-Bashforth scheme. We show that the type of differential operators and the value of orders significantly influence the stability of the Lotka-Volterra system and numerical results demonstrate that different fractional operator derivatives of the nonlinear population model lead to different dynamical behaviors.

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Sene, Ndolane, und José Francisco Gómez Aguilar. „Fractional Mass-Spring-Damper System Described by Generalized Fractional Order Derivatives“. Fractal and Fractional 3, Nr. 3 (07.07.2019): 39. http://dx.doi.org/10.3390/fractalfract3030039.

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This paper proposes novel analytical solutions of the mass-spring-damper systems described by certain generalized fractional derivatives. The Liouville–Caputo left generalized fractional derivative and the left generalized fractional derivative were used. The behaviors of the analytical solutions of the mass-spring-damper systems described by the left generalized fractional derivative and the Liouville–Caputo left generalized fractional derivative were represented graphically and the effect of the orders of the fractional derivatives analyzed. We finish by analyzing the global asymptotic stability and the converging-input-converging-state of the unforced mass-damper system, the unforced spring-damper, the spring-damper system, and the mass-damper system.

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Dissertationen zum Thema "Caputo derivatives"

Oti, Vincent Bediako. „Numerické metody pro řešení počátečních úloh zlomkových diferenciálních rovnic“. Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2021. http://www.nusl.cz/ntk/nusl-445462.

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Tato diplomová práce se zabývá numerickými metodami pro řešení počátečních problémů zlomkových diferenciálních rovnic s Caputovou derivací. Jsou uvedeny dva numerické přístupy spolu s přehledem základních aproximačních formulí. Dvě verze Eulerovy metody jsou realizovány v Matlabu a porovnány na základě numerických experimentů.

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Teodoro, Graziane Sales 1990. „Cálculo fracionário e as funções de Mittag-Leffler“. [s.n.], 2014. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306995.

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Orientador: Edmundo Capelas de Oliveira
Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica
Made available in DSpace on 2018-08-24T12:52:57Z (GMT). No. of bitstreams: 1 Teodoro_GrazianeSales_M.pdf: 8150080 bytes, checksum: 07ef5ddebc25d941750b2dee59bd4022 (MD5) Previous issue date: 2014
Resumo: O cálculo fracionário, nomenclatura utilizada para cálculo de ordem não inteira, tem se mostrado importante e, em muitos casos, imprescindível na discussão de problemas advindos de diversas áreas da ciência, como na matemática, física, engenharia, economia e em muitos outros campos. Neste contexto, abordamos a integral fracionária e as derivadas fracionárias, segundo Caputo e segundo Riemann-Liouville. Dentre as funções relacionadas ao cálculo fracionário, uma das mais importantes é a função de Mittag-Leffler, surgindo naturalmente na solução de várias equações diferenciais fracionárias com coeficientes constantes. Tendo em vista a importância dessa função, a clássica função de Mittag-Leffler e algumas de suas várias generalizações são apresentadas neste trabalho. Na aplicação resolvemos a equação diferencial associada ao problema do oscilador harmônico fracionário, utilizando a transformada de Laplace e a derivada fracionária segundo Caputo
Abstract: The fractional calculus, which is the nomenclature used to the non-integer order calculus, has important applications due to its direct involvement in problem resolution and discussion in many fields, such as mathematics, physics, engineering, economy, applied sciences and many others. In this sense, we studied the fractional integral and fractional derivates: one proposed by Caputo and the other by Riemann-Liouville. Among the fractional calculus's functions, one of most important is the Mittag-Leffler function. This function naturally occurs as the solution for fractional order differential equations with constant coeficients. Due to the importance of the Mittag-Leffler functions, various properties and generalizations are presented in this dissertation. We also presented an application in fractional calculus, in which we solved the differential equation associated the with fractional harmonic oscillator. To solve this fractional oscillator equation, we used the Laplace transform and Caputo fractional derivate
Mestrado
Matematica Aplicada
Mestra em Matemática Aplicada

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Oliveira, Daniela dos Santos de 1990. „Derivada fracionária e as funções de Mittag-Leffler“. [s.n.], 2014. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306994.

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Orientador: Edmundo Capelas de Oliveira
Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica
Made available in DSpace on 2018-08-26T00:53:38Z (GMT). No. of bitstreams: 1 Oliveira_DanieladosSantosde_M.pdf: 3702602 bytes, checksum: c0b05792ff3ac3c5bdd5fad1b7586dd5 (MD5) Previous issue date: 2014
Resumo: Neste trabalho apresentamos um estudo sobre as funções de Mittag-Leffler de um, dois e três parâmetros. Apresentamos a função de Mittag-Leffler como uma generalização da função exponencial bem como a relação que esta possui com outras funções especiais, tais como as funções beta, gama, gama incompleta e erro. Abordamos, também, a integração fracionária que se faz necessária para introduzir o conceito de derivação fracionária. Duas formulações para a derivada fracionária são estudadas, as formulações proposta por Riemann-Liouville e por Caputo. Investigamos quais regras clássicas de derivação são estendidas para estas formulações. Por fim, como uma aplicação, utilizamos a metodologia da transformada de Laplace para resolver a equação diferencial fracionária associada ao problema do oscilador harmônico fracionário
Abstract: This work presents a study about the one- two- and three-parameters Mittag-Leffler functions. We show that the Mittag-Leffler function is a generalization of the exponential function and present its relations to other special functions beta, gamma, incomplete gamma and error functions. We also approach fractional integration, which is necessary to introduce the concept of fractional derivatives. Two formulations for the fractional derivative are studied, the formulations proposed by Riemann-Liouville and by Caputo. We investigate which classical derivatives rules can be extended to these formulations. Finally, as an application, using the Laplace transform methodology, we discuss the fractional differential equation associated with the harmonic oscillator problem
Mestrado
Matematica Aplicada
Mestra em Matemática Aplicada

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Kárský, Vilém. „Modelování LTI SISO systémů zlomkového řádu s využitím zobecněných Laguerrových funkcí“. Master's thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2017. http://www.nusl.cz/ntk/nusl-316278.

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This paper concentrates on the description of fractional order LTI SISO systems using generalized Laguerre functions. There are properties of generalized Laguerre functions described in the paper, and an orthogonal base of these functions is shown. Next the concept of fractional derivatives is explained. The last part of this paper deals with the representation of fractional order LTI SISO systems using generalized Laguerre functions. Several examples were solved to demonstrate the benefits of using these functions for the representation of LTI SISO systems.

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Kadlčík, Libor. „Efektivní použití obvodů zlomkového řádu v integrované technice“. Doctoral thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2020. http://www.nusl.cz/ntk/nusl-432494.

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Integrace a derivace jsou obvykle známy pro celočíselný řád (tj. první, druhý, atd.). Existuje ale zobecnění pro zlomkové (neceločíselné) řády, které lze implementovat pomocí elektronických obvodů zlomkového řádu (případně provést jejich aproximaci) a které poskytuje nový stupeň volnosti pro návrh elektronických obvodů. Obvody zlomkového řádu jsou obvykle aproximovány diskrétními součástkami pomocí RC struktur s velkými rozsahy odporů a kapacit, a tím se jeví nepraktické pro použití v integrovaných obvodech. Tato práce prezentuje implementaci obvodů zlomkového řádu v integerovaných obvodech a jejich praktické využití v této oblasti. Jsou použity prvky se soustředěnými parametry (např. RC žebřík) i prvky s rozprostřenými parametery (např. R-PMOScap, skládající se z nesalicidovaného proužku polykrystalického křemíku nad hradlovým oxidem); je použita pouze technologie typu analogvý CMOS bez dodatečných procesních kroků. Užití obvodů zlomkového řádu bylo demonstrováno realizací několika integrovaných napěťových regulátorů, v nichž obvody zlomkového řádu realizují řízení zlomkového řádu za účelem dosažení silné stejnosměrné regulace a dobré stability regulační smyčky - i bez použití kompenzační nuly nebo příliš vysoké externí kapacity (některé napěťové regulátory dovolují i zatěžovací kapacitou v rozsahu nula až nekonečno).

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Hnaien, Dorsaf. „Equations aux dérivées fractionnaires : propriétés et applications“. Thesis, La Rochelle, 2015. http://www.theses.fr/2015LAROS038.

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Notre objectif dans cette thèse est l'étude des équations différentielles non linéaires comportant des dérivées fractionnaires en temps et/ou en espace. Nous nous sommes intéressés dans un premier temps à l'étude de deux systèmes non linéaires d'équations différentielles fractionnaires en temps et/ou en espace, puis à l'étude d'une équation différentielle fractionnaire en temps. Plus exactement pour la première partie, les questions concernant l'existence globale et le comportement asymptotique des solutions d'un système non linéaire d'équations différentielles comportant des dérivées fractionnaires en temps et en espace sont élucidées. Les techniques utilisées reposent sur des estimations obtenues pour les solutions fondamentales et la comparaison de certaines inégalités fractionnaires. Toujours dans la première partie, l'étude d'un système non linéaire d'équations de réaction-diffusion avec des dérivées fractionnaires en espace est abordée. L'existence locale et l'unicité des solutions sont prouvées à l'aide du théorème du point fixe de Banach. Nous montrons que les solutions sont bornées et analysons leur comportement à l'infini. La deuxième partie est consacrée à l'étude d'une équation différentielle fractionnaire non linéaire. Sous certaines conditions sur la donnée initiale, nous montrons que la solution est globale alors que sous d'autres, elle explose en temps fini. Dans ce dernier cas, nous donnons son profil ainsi que des estimations bilatérales du temps d'explosion. Alors que pour la solution globale nous étudions son comportement asymptotique
Our objective in this thesis is the study of nonlinear differential equations involving fractional derivatives in time and/or in space. First, we are interested in the study of two nonlinear time and/or space fractional systems. Our second interest is devoted to the analysis of a time fractional differential equation. More exactly for the first part, the question concerning the global existence and the asymptotic behavior of a nonlinear system of differential equations involving time and space fractional derivatives is addressed. The used techniques rest on estimates obtained for the fundamental solutions and the comparison of some fractional inequalities. In addition, we study a nonlinear system of reaction-diffusion equations with space fractional derivatives. The local existence and the uniqueness of the solutions are proved using the Banach fixed point theorem. We show that the solutions are bounded and analyze their large time behavior. The second part is dedicated to the study of a nonlinear time fractional differential equation. Under some conditions on the initial data, we show that the solution is global while under others, it blows-up in a finite time. In this case, we give its profile as well as bilateral estimates of the blow-up time. While for the global solution we study its asymptotic behavior

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Ncube, Mahluli Naisbitt. „The natural transform decomposition method for solving fractional differential equations“. Diss., 2018. http://hdl.handle.net/10500/25348.

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In this dissertation, we use the Natural transform decomposition method to obtain approximate analytical solution of fractional differential equations. This technique is a combination of decomposition methods and natural transform method. We use the Adomian decomposition, the homotopy perturbation and the Daftardar-Jafari methods as our decomposition methods. The fractional derivatives are considered in the Caputo and Caputo- Fabrizio sense.
Mathematical Sciences
M. Sc. (Applied Mathematics)

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Toudjeu, Ignace Tchangou. „Mathematical analysis of generalized linear evolution equations with the non-singular kernel derivative“. Diss., 2019. http://hdl.handle.net/10500/25774.

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Linear Evolution Equations (LEE) have been studied extensively over many years. Their extension in the field of fractional calculus have been defined by Dαu(x, t) = Au(x, t), where α is the fractional order and Dα is a generalized differential operator. Two types of generalized differential operators were applied to the LEE in the state-of-the-art, producing the Riemann-Liouville and the Caputo time fractional evolution equations. However the extension of the new Caputo-Fabrizio derivative (CFFD) to these equations has not been developed. This work investigates existing fractional derivative evolution equations and analyze the generalized linear evolution equations with non-singular ker- nel derivative. The well-posedness of the extended CFFD linear evolution equation is demonstrated by proving the existence of a solution, the uniqueness of the existing solu- tion, and finally the continuous dependence of the behavior of the solution on the data and parameters. Extended evolution equations with CFFD are applied to kinetics, heat diffusion and dispersion of shallow water waves using MATLAB simulation software for validation purpose.
Mathematical Science
M Sc. (Applied Mathematics)

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Monyayi, Victor Tebogo. „Well-posedness and mathematical analysis of linear evolution equations with a new parameter“. Diss., 2020. http://hdl.handle.net/10500/26794.

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Abstract in English
In this dissertation we apply linear evolution equations to the Newtonian derivative, Caputo time fractional derivative and $-time fractional derivative. It is notable that the most utilized fractional order derivatives for modelling true life challenges are Riemann- Liouville and Caputo fractional derivatives, however these fractional derivatives have the same weakness of not satisfying the chain rule, which is one of the most important elements of the match asymptotic method [2, 3, 16]. Furthermore the classical bounded perturbation theorem associated with Riemann-Liouville and Caputo fractional derivatives has con rmed not to be in general truthful for these models, particularly for solution operators of evolution systems of a derivative with fractional parameter ' that is less than one (0 < ' < 1) [29]. To solve this problem, we introduce the derivative with new parameter, which is de ned as a local derivative but has a fractional order called $-derivative and apply this derivative to linear evolution equation and to support what we have done in the theory, we utilize application to population dynamics and we provide the numerical simulations for particular cases.
Mathematical Sciences
M.Sc. (Applied Mathematics)

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Buchteile zum Thema "Caputo derivatives"

Anastassiou, George A., und Ioannis K. Argyros. „Iterative Algorithms and Left-Right Caputo Fractional Derivatives“. In Intelligent Numerical Methods: Applications to Fractional Calculus, 231–43. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-26721-0_14.

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Almeida, Ricardo, Agnieszka B. Malinowska und Delfim F. M. Torres. „Fractional Euler–Lagrange Differential Equations via Caputo Derivatives“. In Fractional Dynamics and Control, 109–18. New York, NY: Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4614-0457-6_9.

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Agarwal, Ravi, Snezhana Hristova und Donal O’Regan. „Non-instantaneous Impulses in Differential Equations with Caputo Fractional Derivatives“. In Non-Instantaneous Impulses in Differential Equations, 73–192. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-66384-5_2.

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Chikrii, Arkadii, und Ivan Matychyn. „Riemann–Liouville, Caputo, and Sequential Fractional Derivatives in Differential Games“. In Annals of the International Society of Dynamic Games, 61–81. Boston: Birkhäuser Boston, 2010. http://dx.doi.org/10.1007/978-0-8176-8089-3_4.

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Akdemir, Ahmet Ocak, Hemen Dutta, Ebru Yüksel und Erhan Deniz. „Inequalities for m-Convex Functions via Ψ-Caputo Fractional Derivatives“. In Mathematical Methods and Modelling in Applied Sciences, 215–24. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-43002-3_17.

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Ahmad, Bashir, Ahmed Alsaedi, Sotiris K. Ntouyas und Jessada Tariboon. „Nonlinear Langevin Equation and Inclusions Involving Hadamard-Caputo Type Fractional Derivatives“. In Hadamard-Type Fractional Differential Equations, Inclusions and Inequalities, 209–61. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-52141-1_7.

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D’Abbicco, Marcello. „Critical Exponents for Differential Inequalities with Riemann-Liouville and Caputo Fractional Derivatives“. In Trends in Mathematics, 49–95. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-10937-0_2.

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Lavín-Delgado, J. E., J. E. Solís-Pérez, J. F. Gómez-Aguilar und R. F. Escobar-Jiménez. „Image Edge Detection Using Fractional Conformable Derivatives in Liouville-Caputo Sense for Medical Image Processing“. In Fractional Calculus in Medical and Health Science, 1–54. Boca Raton, FL : CRC Press/Taylor & Francis Group, [2021] |: CRC Press, 2020. http://dx.doi.org/10.1201/9780429340567-1.

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Kashuri, Artion, und Rozana Liko. „Some New Hermite–Hadamard Type Integral Inequalities via Caputo k–Fractional Derivatives and Their Applications“. In Differential and Integral Inequalities, 435–58. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-27407-8_14.

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Atangana, Abdon. „A New Numerical Approximation of Fractional Differentiation: Upwind Discretization for Riemann-Liouville and Caputo Derivatives“. In Nonlinear Systems and Complexity, 193–212. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-90972-1_13.

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Konferenzberichte zum Thema "Caputo derivatives"

Baleanu, Dumitru. „On Constrained Systems Within Caputo Derivatives“. In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-35009.

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The constraints systems play a very important role in physics and engineering. The fractional variational principles were successfully applied to control problems as well as to construct the phase space of a fractional dynamical system. In this paper the fractional dynamics of discrete constrained systems is presented and the notion of the reduced phase-space is analyzed. One system possessing two primary first class constraints is analyzed in detail.

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Baleanu, Dumitru, Sami I. Muslih und Eqab M. Rabei. „On Fractional Hamilton Formulation Within Caputo Derivatives“. In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-34812.

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The fractional Lagrangian and Hamiltonian dynamics is an important issue in fractional calculus area. The classical dynamics can be reformulated in terms of fractional derivatives. The fractional variational principles produce fractional Euler-Lagrange equations and fractional Hamiltonian equations. The fractional dynamics strongly depends of the fractional integration by parts as well as the non-locality of the fractional derivatives. In this paper we present the fractional Hamilton formulation based on Caputo fractional derivatives. One example is treated in details to show the characteristics of the fractional dynamics.

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Trigeassou, Jean-Claude, Nezha Maamri und Alain Oustaloup. „Initialization of Riemann-Liouville and Caputo Fractional Derivatives“. In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-47633.

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Riemann-Liouville and Caputo fractional derivatives are fundamentally related to fractional integration operators. Consequently, the initial conditions of fractional derivatives are the frequency distributed and infinite dimensional state vector of fractional integrators. The paper is dedicated to the estimation of these initial conditions and to the validation of the initialization problem based on this distributed state vector. Numerical simulations applied to Riemann-Liouville and Caputo derivatives demonstrate that the initial conditions problem can be solved thanks to the estimation of the initial state vector of the fractional integrator.

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Narahari Achar, B. N., Carl F. Lorenzo und Tom T. Hartley. „Initialization Issues of the Caputo Fractional Derivative“. In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-84348.

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The importance of proper initialization in taking into account the history of a system whose time evolution is governed by a differential equation of fractional order, has been established by Lorenzo and Hartley, who also gave the method of properly incorporating the effect of the past (history) by means of an initialization function for the Riemann-Liouville and the Grunwald formulations of fractional calculus. The present work addresses this issue for the Caputo fractional derivative and cautions that the commonly held belief that the Caputo formulation of fractional derivatives properly accounts for the initialization effects is not generally true when applied to the solution of fractional differential equations.

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Baleanu, Dumitru, Om P. Agrawal und Sami I. Muslih. „Lagrangians With Linear Velocities Within Hilfer Fractional Derivative“. In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-47953.

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Fractional variational principles started to be one of the major area in the field of fractional calculus. During the last few years the fractional variational principles were developed within several fractional derivatives. One of them is the Hilfer’s generalized fractional derivative which interpolates between Riemann-Liouville and Caputo fractional derivatives. In this paper the fractional Euler-Lagrange equations of the Lagrangians with linear velocities are obtained within the Hilfer fractional derivative.

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Ortigueira, Manuel D. „On the “walking dead” derivatives: Riemann-Liouville and Caputo“. In 2014 International Conference on Fractional Differentiation and its Applications (ICFDA). IEEE, 2014. http://dx.doi.org/10.1109/icfda.2014.6967433.

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Wang, Jie, Jinping Liu, Junbin He, Jianyong Zhu, Tianyu Ma und Zhaohui Tang. „Edge-relevant Structure Feature Detection Using Caputo-Fabrizio Fractional-order Gaussian Derivatives“. In 2019 Chinese Control And Decision Conference (CCDC). IEEE, 2019. http://dx.doi.org/10.1109/ccdc.2019.8832964.

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Li, Xuhao, und Patricia J. Y. Wong. „High order approximation to new generalized Caputo fractional derivatives and its applications“. In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2017). Author(s), 2018. http://dx.doi.org/10.1063/1.5043779.

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AbdelAty, Amr M., Ahmed G. Radwan, Waleed A. Ahmed und Mariam Faied. „Charging and discharging RCα circuit under Riemann-Liouville and Caputo fractional derivatives“. In 2016 13th International Conference on Electrical Engineering/Electronics, Computer, Telecommunications and Information Technology (ECTI-CON). IEEE, 2016. http://dx.doi.org/10.1109/ecticon.2016.7561294.

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Balint, Agneta M., und Stefan Balint. „Objectivity lost when Riemann-Liouville or caputo fractional order derivatives are used“. In TIM 18 PHYSICS CONFERENCE. Author(s), 2019. http://dx.doi.org/10.1063/1.5090070.

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