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Application of Adomian’s Decomposition Method for the Analytical Solution of Space Fractional Diffusion Equation

Author(s): Mohammad Danesh | Mehdi Safari

Journal: Advances in Pure Mathematics
ISSN 2160-0368

Volume: 01;
Issue: 06;
Start page: 345;
Date: 2011;
Original page

Keywords: Adomian’s Decomposition Method | Fractional Derivative | Fractional Diffusion Equation

Spatially fractional order diffusion equations are generalizations of classical diffusion equations which are increasingly used in modeling practical super diffusive problems in fluid flow, finance and others areas of application. This paper presents the analytical solutions of the space fractional diffusion equations by Adomian’s decomposition method (ADM). By using initial conditions, the explicit solutions of the equations have been presented in the closed form. Two examples, the first one is one-dimensional and the second one is two-dimensional fractional diffusion equation, are presented to show the application of the present techniques. The present method performs extremely well in terms of efficiency and simplicity.
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