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I. Podlubny, “An Introduction to Fractional Derivatives, Fractional Differential Equations, Some Methods of Their Solution and Some of Their Applications,” Fractional Differential Equations, Mathematics in Science and Engineering, Vol. 198, Academic Press, San Diego, 1999.

has been cited by the following article:

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

  AUTHORS: Mohammad Danesh, Mehdi Safari

  KEYWORDS: Adomian’s Decomposition Method, Fractional Derivative, Fractional Diffusion Equation

  JOURNAL NAME: Advances in Pure Mathematics, Vol.1 No.6, November 24, 2011

  ABSTRACT: 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.