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R. Metzler and J. Klafter, “The Random Walk’s Guide to Anomalous Diffusion: A Fractional Dynamics Approach,” Physics Reports, Vol. 339, No. 1, 2000, pp. 1-77. doi:10.1016/S0370-1573(00)00070-3

has been cited by the following article:

• TITLE: Application of He’s Variational Iteration Method for the Analytical Solution of Space Fractional Diffusion Equation

  AUTHORS: Mehdi Safari

  KEYWORDS: He’s Variational Iteration Method, Fractional Derivative, Fractional Diffusion Equation

  JOURNAL NAME: Applied Mathematics, Vol.2 No.9, September 19, 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 variational iteration method (VIM). 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.