A new approach in handling one-dimensional time-fractional Schrödinger equations

Abstract

Our aim of this paper was to present the accurate analytical approximate series solutions to the time-fractional Schrödinger equations via the Caputo fractional operator using the Laplace residual power series technique. Furthermore, three important and interesting applications were given, tested, and compared with four well-known methods (Adomian decomposition, homotopy perturbation, homotopy analysis, and variational iteration methods) to show that the proposed technique was simple, accurate, efficient, and applicable. When there was a pattern between the terms of the series, we could obtain the exact solutions; otherwise, we provided the approximate series solutions. Finally, graphical results were presented and analyzed. Mathematica software was used to calculate numerical and symbolic quantities.

Keywords

• fractional operators
• fractional schrödinger equation
• multiple fractional power series
• laplace residual power series method