Dynamics of Damped and Undamped Wave Natures of the Fractional Kraenkel-Manna System in Ferromagnetic Materials

Abstract

This research considers the Kraenkel-Manna-Merle system with an M -truncated derivative (K -M -M -S -M -T -D) that defines the magnetic field propagation (M -F -P) in ferromagnetic materials with zero conductivity (F -M -Z -C) and uses the Sardar subequation method (S -S -E -M). Our goal is to acquire soliton solutions (SSs) of K -M -M -S -M -T -D via the S -S -E -M. To our knowledge, no one has considered the SSs to the K-M-M-S-MTD with or without a damping effect (DE) via the S -S -E -M. The SSs are achieved as the M -shape, periodic wave shape, W -shape, kink, anti -parabolic, and singular kink solitons in terms of free parameters. We utilize Maple to expose pictures in three-dimensional (3-D), contour and two-dimensional (2-D) for different values of fractional order (FO) of the got SSs, and we discuss the effect of the FO of the K-M-M-S-MTD via the S -S -E -M, which has not been discussed in the previous literature. All wave phenomena are applied to optical fiber communication, signal transmission, porous mediums, magneto -acoustic waves in plasma, electromagnetism, fluid dynamics, chaotic systems, coastal engineering, and so on. The achieved SSs prove that the S -S -E -M is very simple and effective for nonlinear science and engineering for examining nonlinear fractional differential equations (N -L -F -D -Es).