Homotopy analysis method with modified Reimann- Liouville derivative for space fractional diffusion equation

In this paper, we applied the homotopy analysis method (HAM) to construct the analytical solutions of the space fractional diffusion equations. The derivatives are defined in the Jumarie’s fractional derivative sense. The explicit solutions of the equations have been presented in the closed form by using initial conditions. Two typical examples have been discussed. The results reveal that the method is very effective and simple. On the basis of computational work and subsequent numerical results, it is worth noting that the advantage of the homotopy analysis methodology is that it displays a fast convergence of the solution.