A new fractional modeling arising in engineering sciences and its analytical approximate solution

The aim of this article is to introduce a new approximate method, namely homotopy perturbation transform method (HPTM) which is a combination of homotopy perturbation method (HPM) and Laplace transform method (LTM) to provide an analytical approximate solution to time-fractional Cauchy-reaction diffusion equation. Reaction diffusion equation is widely used as models for spatial effects in ecology, biology and engineering sciences. A good agreement between the obtained solution and some well-known results has been demonstrated. The numerical solutions obtained by proposed method indicate that the approach is easy to implement and accurate. Some numerical illustrations are given. These results reveal that the proposed method is very effective and simple to perform for engineering sciences problems.