dynamics of damped and undamped wave natures of the fractional kraenkel-manna-merle system in ferromagnetic materials

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 sub-equation 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).