scholarly journals The Numerical Solution of the space-time fractional diffusion equation involving the Caputo-Katugampola fractional derivative

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Kaouther Bouchama ◽  
Yacine Arioua ◽  
Abdelkrim Merzougui
Keyword(s):  
Diffusion Equation ◽  
Fractional Derivative ◽  
Numerical Approximation ◽  
Fractional Diffusion ◽  
Mathematical Induction ◽  
Space Time ◽  
Fractional Diffusion Equation ◽  
Stability And Convergence ◽  
Approximation Solution ◽  
Time Fractional Diffusion Equation

<p style='text-indent:20px;'>In this paper, a numerical approximation solution of a space-time fractional diffusion equation (FDE), involving Caputo-Katugampola fractional derivative is considered. Stability and convergence of the proposed scheme are discussed using mathematical induction. Finally, the proposed method is validated through numerical simulation results of different examples.</p>

On the stable implicit finite differences approximation of diffusion equation with the time fractional derivative without singular kernel

2019 ◽  
Vol 13 (06) ◽  
pp. 2050111 ◽  
Author(s):  
Ali Taghavi ◽  
Afshin Babaei ◽  
Alireza Mohammadpour
Keyword(s):  
Diffusion Equation ◽  
Fractional Derivative ◽  
Finite Differences ◽  
Numerical Approximation ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Stability And Convergence ◽  
Finite Differences Method ◽  
Time Fractional Diffusion Equation ◽  
The Stability

In this paper, we give a numerical approximation to the Caputo–Fabrizio time fractional diffusion equation. The implicit finite differences method is applied to solve a time-fractional diffusion equation with this new fractional derivative. We present the stability and convergence analysis of the proposed numerical scheme. Some numerical problems will be presented to show the accuracy and effectiveness of the method.

NUMERICAL SIMULATIONS FOR SPACE–TIME FRACTIONAL DIFFUSION EQUATIONS

2013 ◽  
Vol 10 (02) ◽  
pp. 1341001 ◽  
Author(s):  
LEEVAN LING ◽  
MASAHIRO YAMAMOTO
Keyword(s):  
Diffusion Equation ◽  
Fractional Derivative ◽  
Time Derivative ◽  
Fundamental Solutions ◽  
Fractional Diffusion ◽  
Space Time ◽  
Fractional Diffusion Equation ◽  
Long Time ◽  
Liouville Fractional Derivative ◽  
Time Fractional Diffusion Equation

We consider the solutions of a space–time fractional diffusion equation on the interval [-1, 1]. The equation is obtained from the standard diffusion equation by replacing the second-order space derivative by a Riemann–Liouville fractional derivative of order between one and two, and the first-order time derivative by a Caputo fractional derivative of order between zero and one. As the fundamental solution of this fractional equation is unknown (if exists), an eigenfunction approach is applied to obtain approximate fundamental solutions which are then used to solve the space–time fractional diffusion equation with initial and boundary values. Numerical results are presented to demonstrate the effectiveness of the proposed method in long time simulations.

scholarly journals Semianalytic Solution of Space-Time Fractional Diffusion Equation

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
A. Elsaid ◽  
S. Shamseldeen ◽  
S. Madkour
Keyword(s):  
Diffusion Equation ◽  
Fractional Derivative ◽  
Time Derivative ◽  
Fractional Diffusion ◽  
Space Time ◽  
Fractional Diffusion Equation ◽  
Optimal Homotopy Analysis Method ◽  
Homotopy Analysis ◽  
Time Fractional Diffusion Equation ◽  
Fractional Time Derivative

We study the space-time fractional diffusion equation with spatial Riesz-Feller fractional derivative and Caputo fractional time derivative. The continuation of the solution of this fractional equation to the solution of the corresponding integer order equation is proved. The series solution of this problem is obtained via the optimal homotopy analysis method (OHAM). Numerical simulations are presented to validate the method and to show the effect of changing the fractional derivative parameters on the solution behavior.

scholarly journals A novel series method for fractional diffusion equation within Caputo fractional derivative

2016 ◽  
Vol 20 (suppl. 3) ◽  
pp. 695-699 ◽  
Author(s):  
Sheng-Ping Yan ◽  
Wei-Ping Zhong ◽  
Xiao-Jun Yang
Keyword(s):  
Diffusion Equation ◽  
Fractional Derivative ◽  
Caputo Fractional Derivative ◽  
Series Solution ◽  
Expansion Method ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Series Method ◽  
Time Fractional Diffusion Equation ◽  
Series Expansion Method

In this paper, we suggest the series expansion method for finding the series solution for the time-fractional diffusion equation involving Caputo fractional derivative.

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