New optical soliton solutions for nonlinear complex fractional Schrödinger equation via new auxiliary equation method and novel $$({G'}/{G})$$ ( G ′ / G ) -expansion method

Abstract

In this research, we apply two different techniques on nonlinear complex fractional nonlinear Schrodinger equation which is a very important model in fractional quantum mechanics. Nonlinear Schrodinger equation is one of the basic models in fibre optics and many other branches of science. We use the conformable fractional derivative to transfer the nonlinear real integer-order nonlinear Schrodinger equation to nonlinear complex fractional nonlinear Schrodinger equation. We apply new auxiliary equation method and novel $$\left( {G'}/{G}\right) $$ -expansion method on nonlinear complex fractional Schrodinger equation to obtain new optical forms of solitary travelling wave solutions. We find many new optical solitary travelling wave solutions for this model. These solutions are obtained precisely and efficiency of the method can be demonstrated.