Application of modified decomposition method for the analytical solution of space fractional diffusion equation

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 Modified decomposition method (MDM). By using initial conditions, the explicit solutions of the equations have been presented in the closed form. The decomposition series analytic solution of the problem is quickly obtained by observing the existence of the self-cancelling “noise” phenomenon. 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 technique. The present method performs extremely well in terms of efficiency and simplicity.