On the solution of the space-time fractional cubic nonlinear Schrödinger equation

Abstract

The space–time fractional nonlinear Schrödinger equation is studied based on the modified Riemann–Liouville derivative. The fractional mapping expansion method is used to find analytical solution of this model. We discuss the effects of the fractional differential order on the W-soliton and bright soliton solutions. The derived solutions show direct proportionality between soliton intensities and the value of the fractional order derivative. Keywords: Fractional mapping expansion method, Nonlinear fractional differential equation, Modified Riemann–Liouville derivative, Space-time fractional nonlinear Schrödinger equation