Approximate analytical solutions of fractional nonlinear Schrodinger equations using multistep modified reduced differential transform method

Abstract

In this paper, we propose and execute the Multistep Modified Reduced Differential Transform Method (MMRDTM) to obtain the solution of fractional nonlinear Schrodinger equations (FNLSEs). Using this proposed technique, the nonlinear term is substituted by the related Adomian polynomials followed by application of a multistep approach. In addition, the fractional NLSE solutions can be obtained with less computational effort than other approximate analytical solution such as Adomian decomposition method, homotopy pertubation method, variational iteration method and differential transformation method. Besides that, it offers precise estimated solutions over a longer time period. We considered a few FNLSEs and represent the features of these solutions in the form of graphs to demonstrate the power and precision of the MMRDTM.