Results 11 to 20 of about 615,518 (166)

The general Caputo–Katugampola fractional derivative and numerical approach for solving the fractional differential equations

Alexandria Engineering Journal
In this manuscript, we present the general fractional derivative (FD) along with its fractional integral (FI), specifically the ψ-Caputo–Katugampola fractional derivative (ψ-CKFD).
Lakhlifa Sadek, Sahar Ahmed ldris, Fahd Jarad   +2 more
doaj   +2 more sources

Galerkin Finite Element Method for Caputo–Hadamard Time-Space Fractional Diffusion Equation

Mathematics
In this paper, we study the Caputo–Hadamard time-space fractional diffusion equation, where the Caputo derivative is defined in the temporal direction and the Hadamard derivative is defined in the spatial direction separately.
Zhengang Zhao, Yunying Zheng
doaj   +2 more sources

Logarithmic Bernstein functions for fractional Rosenau–Hyman equation with the Caputo–Hadamard derivative [PDF]

Results in Physics
In this study, the Caputo–Hadamard derivative is fittingly used to define a fractional form of the Rosenau–Hyman equation. To solve this equation, the orthonormal logarithmic Bernstein functions (BFs) are created as a suitable basis for handling this ...
M.H. Heydari, F. Heydari, O. Bavi, M. Bayram   +3 more
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Perturbed functional fractional differential equation of Caputo-Hadamard order [PDF]

Mathematica Moravica
In this paper, we investigate the existence of solution and extremal solutions for an initial-value problem of perturbed functional fractional differential equations with Caputo-Hadamard derivative.
Hamani Samira
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Hyers-Ulam-Rassias Stability of some sequential neutral functional differential equations with Caputo-Hadamard fractional derivative [PDF]

Miskolc Mathematical Notes
In this article, we employ a fixed point theory to investigate the stability in the sense of Hyers-Ulam-Rassias of some sequential neutral functional differential equations with Caputo-Hadamard fractional derivative. We present two examples to illustrate
Abdellatif Ben Makhlouf, El-sayed El-hady   +1 more
doaj   +2 more sources

Stability for Caputo–Hadamard Fractional Uncertain Differential Equation

Fractal and Fractional
This paper focuses on the Caputo-Hadamard fractional uncertain differential equations (CH-FUDEs) governed by Liu processes, which combine the Caputo–Hadamard fractional derivative with uncertain differential equations to describe dynamic systems ...
Shida Peng, Zhi Li, Jun Zhang, Yuncong Zhu, Liping Xu   +4 more
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Survey and new results on boundary-value problems of singular fractional differential equations with impulse effects

Electronic Journal of Differential Equations, 2016
Firstly we prove existence and uniqueness of solutions of Cauchy problems of linear fractional differential equations (LFDEs) with two variable coefficients involving Caputo fractional derivative, Riemann-Liouville derivative, Caputo type Hadamard ...
Yuji Liu
doaj   +1 more source

Jacobi polynomials method for a coupled system of Hadamard fractional Klein–Gordon–Schrödinger equations

Alexandria Engineering Journal
In this work, the Caputo-type Hadamard fractional derivative is utilized to introduce a coupled system of time fractional Klein–Gordon-Schrödinger equations.
M.H. Heydari, M. Razzaghi
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Shifted Chebyshev polynomials method for Caputo-Hadamard fractional Ginzburg–Landau equation

Results in Physics
This paper introduces a fractional version of the Ginzberg–Landau equation utilizing the Caputo-Hadamard derivative. To address this problem, a numerical method based on the shifted Chebyshev polynomials is developed.
M.H. Heydari, F. Rostami, M. Bayram, D. Baleanu   +3 more
doaj   +2 more sources

Discrete Legendre polynomials method to solve the coupled nonlinear Caputo–Hadamard fractional Ginzburg–Landau equations

Results in Physics
This paper employs the Caputo–Hadamard derivative to create the coupled nonlinear fractional Ginzburg–Landau equations. An orthonormal version of the discrete Legendre polynomials is utilized to generate a numerical strategy for this system.
M.H. Heydari, D. Baleanu, M. Bayram
doaj   +2 more sources