Exact Solutions of the Paraxial Wave Dynamical Model in Kerr Media with Truncated M-fractional Derivative using the (G′/G, 1/G)-Expansion Method

Abstract

The main purpose of this article is to use the (G′/G, 1/G)-expansion method to derive exact traveling wave solutions of the paraxial wave dynamical model in Kerr media in the sense of the truncated M-fractional derivative. To the best of the authors’ knowledge, the solutions of the model obtained using the expansion method are reported here for the first time. The exact solutions are complex-valued functions expressed in terms of hyperbolic, trigonometric, and rational functions. In order to show the physical interpretations of the solutions, the magnitude of selected solutions is plotted in 3D, 2D, and contour plots for a range of values of the fractionalorder of the equation. With the aid of a symbolic software package, all of the obtained solutions are substituted back into the relevant equation to verify their correctness. Obtaining the results by this technique confirms the strength and efficacy of the method for generating a variety of exact solutions of the problems arising in applied sciences and engineering.