A New Approximate Solution of Time-Fractional, Non-linear Schrodinger Equations Using Fractional Reduced Differential Transformation

TL;DR

This paper introduces a fractional reduced differential transform method to efficiently find approximate solutions for time-fractional nonlinear Schrödinger equations, demonstrating rapid convergence and computational simplicity compared to existing methods.

Contribution

The paper presents a novel fractional reduced differential transform approach for solving time-fractional nonlinear Schrödinger equations, offering faster convergence and reduced computational effort.

Findings

Solutions converge rapidly to the exact solution.

Method is easier to apply and requires less computation.

Results agree well with other established methods.

Abstract

This paper is concerned with an alternative analytical solution of time-fractional nonlinear Schrodinger equation and nonlinear coupled Schrodinger equation obtained by employing fractional reduced differential transform method. The proposed solutions are obtained in series form, converges to the exact solution very rapidly. These results are agreed well with the results obtained by using differential transform method, homotopy perturbation method, homotopy analysis method and Adomian decomposition method. However, the computations shows that the described method is easy to apply, and it needs small size of computation contrary to the existing above said methods.