New soliton solutions of kraenkel-manna-merle system with beta time derivative

Abstract

This article discusses the fractional Kraenkel-Manna-Merle (KMM) system, which describes the motion of a nonlinear ultrashort wave pulse through saturated ferromagnetic materials with zero conductivity. The fractional behavior of this system was investigated using the beta derivative. The modified generalized exponential rational function method (MGERFM), developed by modifying the generalized exponential rational function method (GERFM), is applied to this system for the first time. Thus, some soliton solutions of the KMM system that have not been obtained before are presented for the first time in this study. In addition, 2D, 3D and density graphs of the obtained solutions for various values and ranges are presented. Discussions of these graphs are given and the found solutions are compared with other solutions.