Numerical investigation of the two-dimensional space-time fractional diffusion equation in porous media

2021 ◽  
Author(s):  
B. Farnam ◽  
Y. Esmaeelzade Aghdam ◽  
O. Nikan
Keyword(s):  
Porous Media ◽  
Diffusion Equation ◽  
Numerical Investigation ◽  
Dimensional Space ◽  
Fractional Diffusion ◽  
Space Time ◽  
Fractional Diffusion Equation ◽  
Two Dimensional ◽  
Dimensional Space Time ◽  
Time Fractional Diffusion Equation

scholarly journals Subordination Approach to Space-Time Fractional Diffusion

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 415 ◽  
Author(s):  
Emilia Bazhlekova ◽  
Ivan Bazhlekov
Keyword(s):  
Fundamental Solution ◽  
Diffusion Equation ◽  
Numerical Evaluation ◽  
Dimensional Space ◽  
Gaussian Function ◽  
Fractional Diffusion ◽  
Space Time ◽  
Integral Representations ◽  
Dimensional Space Time ◽  
Time Fractional Diffusion Equation

The fundamental solution to the multi-dimensional space-time fractional diffusion equation is studied by applying the subordination principle, which provides a relation to the classical Gaussian function. Integral representations in terms of Mittag-Leffler functions are derived for the fundamental solution and the subordination kernel. The obtained integral representations are used for numerical evaluation of the fundamental solution for different values of the parameters.

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.

Sign in / Sign up

Export Citation Format

Share Document