Results 171 to 180 of about 577,075 (200)

AsymptotIc Behavior of Solutions of Fractional Differential Equations with Hadamard Fractional Derivatives

Fractional Calculus and Applied Analysis, 2021
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Kassim, Mohammed D., Tatar, Nasser-eddine   +1 more
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Extremum Principle for the Hadamard Derivatives and Its Application to Nonlinear Fractional Partial Differential Equations

Fractional Calculus and Applied Analysis, 2019
In this paper we obtain new estimates of the Hadamard fractional derivatives of a function at its extreme points. The extremum principle is then applied to show that the initial-boundary-value problem for linear and nonlinear time-fractional diffusion ...
Berikbol T. Torebek, Mokhtar Kirane
exaly   +2 more sources

Blowup for semilinear fractional diffusion system with Caputo–Hadamard derivative

Mathematical Methods in the Applied Sciences, 2022
The main aim of this paper is to study the blowing‐up behavior of the solution for semilinear fractional diffusion system with the Caputo–Hadamard derivative and the fractional Laplacian. We construct a mild solution of the semilinear system by using the fundamental solutions and then prove the local existence and uniqueness of the mild solution by ...
Jinping Yang, Zhiqiang Li
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Chaos Detection of the Chen System with Caputo–Hadamard Fractional Derivative

International Journal of Bifurcation and Chaos, 2021
In this paper, we investigate the chaotic behaviors of the Chen system with Caputo–Hadamard derivative. First, we construct some practical numerical schemes for the Chen system with Caputo–Hadamard derivative. Then, by means of the variational equation, we estimate the bounds of the Lyapunov exponents for the considered system.
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Sequential fractional differential equations with Hadamard derivative

Communications in Nonlinear Science and Numerical Simulation, 2011
The existence and uniqueness of the solution to an initial value problem for a class of nonlinear sequential fractional differential equations is investigated by means of Banach's fixed point theorem. An example is presented to illustrate the main result.
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Cauchy problems involving a Hadamard-type fractional derivative

Mathematica Slovaca, 2018
Abstract In this paper, we investigate some Cauchy problems involving a left-sided Hadamard-type fractional derivative. A theorem on the existence of a unique solution to a nonlinear problem is proved. The main result is obtained using a fixed point theorem due to Banach, as well as the Bielecki norm. A Cauchy formula for the solution of
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Existence Theory for a Fractional Order System Governed by the Hadamard-Caputo Derivative

Journal of Applied Mathematics and Computing
Thabet Abdeljawad, Anoop Kumar
exaly   +4 more sources

On Hadamard and Fej\'{e}r--Hadamard inequalities for Caputo $\small{k}$-fractional derivatives

2018
In this paper we will prove certain Hadamard and Fejer-Hadamard inequalities for the functions whose nth derivatives are convex by using Caputo k-fractional derivatives. These results have some relationship with inequalities for Caputo fractional derivatives.
Farid, Ghulam, Javed, Anum
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Solvability of a Hadamard fractional boundary value problem with multi‐term integral and Hadamard fractional derivative boundary conditions

Mathematical Methods in the Applied Sciences
In the present paper, we construct the existence of nontrivial solutions to a new kind of Hadamard fractional boundary value problem on an unbounded domain. With the contribution of some fixed point theorems in cone and the corresponding Green function, we ensure sufficient conditions for the Hadamard fractional boundary value problem.
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A High Order Scheme for Fractional Differential Equations with the Caputo-Hadamard Derivative

Journal of Computational Mathematics
In this paper, we consider numerical solutions of the fractional diffusion equation with the $α$ order time fractional derivative defined in the Caputo-Hadamard sense. A high order time-stepping scheme is constructed, analyzed, and numerically validated.
Ye, Xingyang, Cao, Junying, Xu, Chuanju
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