Nonlinear Schrödinger equation under non-singular fractional operators: A computational study

Abstract

In this article, we present study on time fractional nonlinear Schrödinger equation. We investigate the behaviour of the aforesaid equation in two numerous types of operators having non-singular kernels, which are Atangana–Baleanu and Caputo–Fabrizio operators both considered in Caputo’s sense. The considered operators are very useful as they present tremendous dynamics of the suggested equation. We obtain numerical and analytical solutions of the proposed equation under the aforementioned fractional operators by modified double Laplace transform. We present the error analysis of the suggested scheme, where we observed that the considered system primarily depend on time. When time is small, we obtain very small error between the exact and approximate solutions. For the efficiency of our considered scheme, we present some examples. Further, we present the graphical and numerical analysis of the scheme used for the solution.

Keywords

• Schrödinger equation
• Double Laplace transform
• Atangana–Baleanu operator
• Caputo–Fabrizio operator