Results 41 to 50 of about 39,585 (286)

On Caputo modification of the Hadamard fractional derivatives [PDF]

Advances in Difference Equations, 2014
Abstract This paper is devoted to the study of Caputo modification of the Hadamard fractional derivatives. From here and after, by Caputo-Hadamard derivative, we refer to this modified fractional derivative (Jarad et al. in Adv. Differ. Equ. 2012:142, 2012, p.7). We present the generalization of the fundamental theorem of fractional calculus (
Yusuf Y. Gambo, Fahd Jarad, Dumitru Băleanu, Thabet Abdeljawad   +3 more
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Comparison of third-order fractional partial differential equation based on the fractional operators using the explicit finite difference method

Alexandria Engineering Journal, 2023
In this research paper, the third-order fractional partial differential equation (FPDE) in the sense of the Caputo fractional derivative and the Atangana-Baleanu Caputo (ABC) fractional derivative is investigated for the first time. The importance of the
Shorish Omer Abdulla, Sadeq Taha Abdulazeez, Mahmut Modanli   +2 more
doaj   +1 more source

Laplace Variational Iteration Method for Modified Fractional Derivatives with Non-singular Kernel [PDF]

Journal of Applied and Computational Mechanics, 2020
A universal approach by Laplace transform to the variational iteration method for fractional derivatives with the nonsingular kernel is presented; in particular, the Caputo-Fabrizio fractional derivative and the Atangana-Baleanu fractional derivative ...
Huitzilín Yépez-Martínez, José Francisco Gómez-Aguilar   +1 more
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Analyzing transient response of the parallel RCL circuit by using the Caputo–Fabrizio fractional derivative

, 2020
In this paper, the transient response of the parallel RCL circuit with Caputo–Fabrizio derivative is solved by Laplace transforms. Also, the graphs of the obtained solutions for the different orders of the fractional derivatives are compared with each ...
Shahram Alizadeh, D. Baleanu, S. Rezapour   +2 more
semanticscholar   +1 more source

Approximations for the Caputo derivative (II)

, 2016
In the present paper we use the expansion formula of the polylogarithm function to construct approximations of the Caputo derivative which are related to the midpoint approximation of the integral in the definition of the Caputo derivative. The asymptotic expansion formula of the Riemann sum approximation of the beta function and the first terms of the
Dimitrov, Yuri, Todorov, Venelin, Miryanov, Radan   +2 more
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Modeling blood alcohol concentration using fractional differential equations based on the ψ‐Caputo derivative [PDF]

Mathematical methods in the applied sciences
We propose a novel dynamical model for blood alcohol concentration that incorporates ψ$$ \psi $$ ‐Caputo fractional derivatives. Using the generalized Laplace transform technique, we successfully derive an analytic solution for both the alcohol ...
O. Wanassi, Delfim F. M. Torres
semanticscholar   +1 more source

On the chaotic nature of the Rabinovich system through Caputo and Atangana–Baleanu–Caputo fractional derivatives

Advances in Continuous and Discrete Models, 2022
AbstractThe Rabinovich system can describe different physical interactions, including waves in plasmas, a convective fluid flow inside a rotating ellipsoid, and Kolmogorov’s flow interactions. This study considers the Rabinovich system through Caputo and Atangana–Baleanu fractional derivatives to detect its chaotic nature.
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On applications of Caputo k-fractional derivatives

Advances in Difference Equations, 2019
This research explores Caputo k-fractional integral inequalities for functions whose nth order derivatives are absolutely continuous and possess Grüss type variable bounds. Using Chebyshev inequality (Waheed et al. in IEEE Access 7:32137–32145, 2019) for
Ghulam Farid, Naveed Latif, Matloob Anwar, Ali Imran, Muhammad Ozair, Madeeha Nawaz   +5 more
doaj   +1 more source

The k-fractional logistic equation with k-Caputo derivative [PDF]

Pure Mathematical Sciences, 2015
Fil: Cerutti, Ruben A. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas y Naturales y Agrimensura; Argentina.
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Fractional Differential Equations With Dependence on the Caputo–Katugampola Derivative [PDF]

Journal of Computational and Nonlinear Dynamics, 2016
In this paper, we present a new type of fractional operator, the Caputo–Katugampola derivative. The Caputo and the Caputo–Hadamard fractional derivatives are special cases of this new operator. An existence and uniqueness theorem for a fractional Cauchy-type problem, with dependence on the Caputo–Katugampola derivative, is proved.
Almeida, R., Malinowska, A. B., Odzijewicz, T.   +2 more
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