Results 171 to 180 of about 615,568 (200)

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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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
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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
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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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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
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Efficient spectral collocation method for fractional differential equation with Caputo-Hadamard derivative

Fractional Calculus and Applied Analysis, 2023
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Tinggang Zhao, Changpin Li, Dongxia Li
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Coupled fractional differential equations involving Caputo–Hadamard derivative with nonlocal boundary conditions

Mathematical Methods in the Applied Sciences, 2020
This paper aims to study the sufficient conditions for the existence and uniqueness of solutions to the multipoint coupled boundary value problem of nonlinear Caputo–Hadamard fractional differential equations associating with nonlocal integral boundary conditions.
Ankit Nain, Ramesh Vats, Avadhesh Kumar
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A High Order Scheme for Fractional Differential Equations with the Caputo-Hadamard Derivative

Journal of Computational Mathematics
Summary: In this paper, we consider numerical solutions of the fractional diffusion equation with the \(\alpha\) 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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Ulam-Hyers stability of uncertain functional differential equation in fuzzy setting with Caputo-Hadamard fractional derivative concept

Journal of Intelligent & Fuzzy Systems, 2019
 In this work, by using the Caputo-Hadamard fractional derivative concept, we propose a new class of fuzzy functional differential equation. In this sense, we establish the existence of the solution, the Ulam-Hyers stability and the Ulam-Hyers-Mittag-Leffler stability for the given problem by means of successive approximation method.
Ho Vu 0001, Truong Vinh An, Ngo Van Hoa
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Dynamical Features and Complete Synchronization of Unified Chaotic Systems With Caputo-Hadamard Fractional Derivative

Journal of Computational and Nonlinear Dynamics
Abstract This paper investigates the dynamical characteristics and synchronization of a unified chaotic system described by Caputo–Hadamard fractional derivative. The equilibrium solutions of the considered system are first analyzed and confirmed to be unstable. Then, by observing the phase diagram and calculating the largest Lyapunov
Chuntao Yin, Yufei Zhao, Yangquan Chen, Yongjun Shen   +3 more
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