Results 171 to 180 of about 582,712 (204)

Some results for a class of delayed fractional partial differential equations with Caputo–Hadamard derivative

Mathematical Methods in the Applied Sciences, 2023
In this paper, we study the existence and uniqueness of the global solution to the Fractional Hyperbolic Systems of Partial Differential equations (FHyPDifS) by the Caputo–Hadamard fractional‐order derivative. In addition, we give a new sufficient conditions for the finite time stability (FTS) of FHyPDifS for the Caputo–Hadamard fractional‐order ...
Hassen Arfaoui
exaly   +3 more sources

On a Caputo-type fractional derivative

Advances in Pure and Applied Mathematics, 2019
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.
Edmundo Capelas de Oliveira
exaly   +3 more sources

Numerical Methods for Caputo–Hadamard Fractional Differential Equations with Graded and Non-Uniform Meshes [PDF]

Mathematics, 2021
We consider the predictor-corrector numerical methods for solving Caputo–Hadamard fractional differential equations with the graded meshes logtj=loga+logtNajNr,j=0,1,2,…,N with a≥1 and r≥1, where loga=logt0logt1⋯logtN=logT is a partition of [logt0,logT].
Yubin Yan
exaly   +3 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
openaire   +1 more source

Halanay inequality involving Caputo-Hadamard fractional derivative and application

International Journal of Nonlinear Sciences and Numerical Simulation, 2022
Abstract A Halanay inequality with distributed delay of non-convolution type is considered. We establish a decay of solutions as a Mittag-Leffler function composed with a logarithmic function. A general sufficient condition is found and a large class of admissible retardation kernels is provided.
Mohammed D. Kassim, Nasser-eddine Tatar
openaire   +2 more sources

MILD SOLUTIONS OF COUPLED HYBRID FRACTIONAL ORDER SYSTEM WITH CAPUTO–HADAMARD DERIVATIVES

Fractals, 2021
This paper is devoted to prove the existence of mild solutions of coupled hybrid fractional order system with Caputo–Hadamard derivatives using Dhage fixed point theorem in Banach algebras. In order to confirm the applicability of obtained result an example is also presented.
Bedi, Pallavi, Kumar, Anoop, Abdeljawad, Thabet, Khan, Aziz, Gómez-Aguilar, J. F.   +4 more
openaire   +1 more source

Numerical approaches to Caputo–Hadamard fractional derivatives with applications to long-term integration of fractional differential systems

Communications in Nonlinear Science and Numerical Simulation, 2022
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Enyu Fan, Changpin Li, Zhiqiang Li
openaire   +2 more sources

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.
openaire   +2 more sources

Stability for coupled systems on networks with Caputo-Hadamard fractional derivative

2021
Summary: This paper discusses stability and uniform asymptotic stability of the trivial solution of the following coupled systems of fractional differential equations on networks \[ \left\{\begin{array}{lll} ^{cH}D^{\alpha}x_i=f_i(t,x_i)+\sum\limits_{j=1}^ng_{ij}(t,x_i,x_j),\quad t>t_0,\\ x_i(t_0)=x_{i0}, \end{array}\right. \] where \(^{cH}D^{\alpha}\)
Belbali, Hadjer, Benbachir, Maamar
openaire   +1 more source

Temporal discretization for Caputo–Hadamard fractional derivative with incomplete Gamma function via Whittaker function

Computational and Applied Mathematics, 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yoke Teng Toh, Chang Phang, Yong Xian Ng
openaire   +2 more sources