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Regional gradient controllability of ultra-slow diffusions involving the Hadamard-Caputo time fractional derivative [PDF]

Mathematical Control and Related Fields, 2020
This paper investigates the regional gradient controllability for ultra-slow diffusion processes governed by the time fractional diffusion systems with a Hadamard-Caputo time fractional derivative.
Ruiyang Cai, Chunhai Kou, Fudong Ge
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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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Dependence of solutions on the order of the Caputo-Hadamard derivative and illustrative examples

Fractional Calculus and Applied Analysis
Nguyen Huu Can
exaly   +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
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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.
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
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Temporal discretization for Caputo–Hadamard fractional derivative with incomplete Gamma function via Whittaker function

Computational and Applied Mathematics, 2021
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Yoke Teng Toh, Chang Phang, Yong Xian Ng
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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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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
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