The improved HPM for analytical solution of fractional Schr\"{o}dinger equation

Abstract

We have applied the new approach of homotopy perturbation method (\textit{NHPM}) for Schr\"{o}dinger equation featuring time-fractional derivative. A combination of \textit{NHPM} and multiple fractional power series form has been used the first time to present analytical solution. In order to illustrate the simplicity and ability of the suggested approach, some specific and clear examples have been given. All numerical calculations in this manuscript have been carried out with $ Mathematica $.