A fractional model of the diffusion equation and its analytical solution using Laplace transform

In this study, the homotopy perturbation transform method (HPTM) is performed to give analytical solutions of the time fractional diffusion equation. The HPTM is a combined form of the Laplace transform and homotopy perturbation methods. The numerical solutions obtained by the proposed method indicate that the approach is easy to implement and accurate. These results reveal that the proposed method is very effective and simple in performing a solution to the fractional partial differential equation. A solution has been plotted for different values of :, and some numerical illustrations are given.