Residual power series method for fractional diffusion equations

In this article, improved residual power series method (RPSM) is effectively implemented to find the approximate analytical solution of a time fractional diffusion equations. The proposed method is an analytic technique based on the generalized Taylor's series formula which construct an analytical solution in the form of a convergent series. In order to illustrate the advantages and the accuracy of the RPSM, we have applied the method to two different examples. In case of first example, different cases of initial conditions are considered. Finally, the solutions of the time fractional diffusion equations are investigate through graphical representation, which interpret simplicity, accuracy and practical usefulness of the present method.