scholarly journals Numerical Approximation for Fractional Diffusion Equation Forced by a Tempered Fractional Gaussian Noise

2020 ◽  
Vol 84 (1) ◽  
Author(s):  
Xing Liu ◽  
Weihua Deng
Keyword(s):  
Diffusion Equation ◽  
Gaussian Noise ◽  
Numerical Approximation ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Fractional Gaussian Noise

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.

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>

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