Solving Fractional Schrödinger Equations via Homotopy Perturbation Sumudu Transform Method

Abstract

We propose and analyze a technique that combines the homotopy perturbation method and the Sumudu transform method. This method is called the homotopy perturbation Sumudu transform method. We use this method to solve the generalized time-space fractional Schrödinger equation. The fractional derivative is described in the Caputo sense. The proposed scheme finds the solution without any discretization, transformation, or restrictive assumptions. We present several examples to verify the reliability and efficiency of the proposed technique.