Results 81 to 90 of about 388,923 (185)

An Extension of the Picard Theorem to Fractional Differential Equations with a Caputo-Fabrizio Derivative

, 2021
In this paper, we consider fractional differential equations with the new fractional derivative involving a nonsingular kernel, namely, the Caputo-Fabrizio fractional derivative.
H. R. Marasi, H. Aydi, A. Soltani Joujehi   +2 more
core   +1 more source

Existence and uniqueness of solutions to fractional differential equations in the frame of generalized Caputo fractional derivatives

Advances in Difference Equations, 2018
The generalized Caputo fractional derivative is a name attributed to the Caputo version of the generalized fractional derivative introduced in Jarad et al. (J. Nonlinear Sci. Appl. 10:2607–2619, 2017).
Y. Y. Gambo, R. Ameen, F. Jarad, T. Abdeljawad   +3 more
doaj   +1 more source

New integral inequalities for s-convex functions of the second sense via the caputo fractional derivative and the caputo–fabrizio integral operator

, 2023
Various integral inequalities for s-convex functions in the second sense are obtained by means of the Caputo fractional derivative and the Caputo–Fabrizio integral operator.
Yeşi̇lce Işık, İlknur, Tinaztepe, Gülteki̇n, Kemalı, Serap, Sezer Evcan, Si̇nem   +3 more
core   +1 more source

A highly accurate method for multi-term time fractional diffusion equation in two dimensions with ψ-Caputo fractional derivative

Results in Applied Mathematics
In this study, the ψ-Caputo fractional derivative (as a generalization of the classical Caputo derivative where the fractional derivative is defined with respect to the function ψ) is considered to introduce a class of multi-term time fractional 2D ...
M.H. Heydari, M. Razzaghi
doaj   +1 more source

Time fractional IHCP with Caputo fractional derivatives

Computers & Mathematics with Applications, 2008
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +2 more sources

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.
openaire   +1 more source

A discrete spectral method for time fractional fourth-order 2D diffusion-wave equation involving ψ-Caputo fractional derivative

Results in Applied Mathematics
In this work, the ψ-Caputo fractional derivative, as a generalization of the classical Caputo fractional derivative in which the fractional derivative of a sufficiently differentiable function is defined with respect to another strictly increasing ...
M.H. Heydari, M. Razzaghi
doaj   +1 more source

Fractional Cauchy Problem with Caputo Nabla Derivative on Time Scales [PDF]

, 2020
The definition of Caputo fractional derivative is given and some of its properties are discussed in detail. After then, the existence of the solution and the dependency of the solution upon the initial value for Cauchy type problem with fractional Caputo
Jiang Zhu, Ling Wu
core  

‐Caputo derivative and their applications

, 2021
Systems of fractional differential equations with a general form of fractional derivative are considered. A unique continuous solution is derived using the Banach fixed point theorem.
Odzijewicz, Tatiana, Malinowska, Agnieszka B., Agnieszka B. Malinowska, Almeida, Ricardo, Tatiana Odzijewicz, Ricardo Almeida   +5 more
core   +1 more source

Cauchy problem for fractional evolution equations with Caputo derivative

, 2013
This paper concerns the abstract nonlocal Cauchy problem of a class of fractional evolution equations with Caputo derivative. A suitable mild solution of evolution equations with Caputo derivative is introduced.
X.H. Shen, L. Zhang, Y. Zhou
core   +1 more source