Analytical Approximate Solution of Space-Time Fractional Diffusion Equation with a Moving Boundary Condition

2011 ◽  
Vol 66 (5) ◽  
pp. 281-288 ◽  
Author(s):  
Subir Das ◽  
Rajnesh Kumar ◽  
Praveen Kumar Gupta
Keyword(s):  
Diffusion Equation ◽  
Moving Boundary ◽  
Numerical Solutions ◽  
Fractional Diffusion ◽  
Space Time ◽  
Fractional Diffusion Equation ◽  
Approximate Analytic Solution ◽  
Approximate Analytical Solutions ◽  
Moving Boundary Condition ◽  
Time Fractional Diffusion Equation

August 12, 2010 The homotopy perturbation method is used to find an approximate analytic solution of the problem involving a space-time fractional diffusion equation with a moving boundary. This mathematical technique is used to solve the problem which performs extremely well in terms of efficiency and simplicity. Numerical solutions of the problem reveal that only a few iterations are needed to obtain accurate approximate analytical solutions. The results obtained are presented graphically.

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.

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