%0 Journal Article
%T Dynamics of Damped and Undamped Wave Natures of the Fractional Kraenkel-Manna-Merle System in Ferromagnetic Materials
%J Journal of Applied and Computational Mechanics
%I Shahid Chamran University of Ahvaz
%Z 2383-4536
%A Alam, Md. Nur
%A Rahim, Md. Abdur
%A Hossain, Md. Najmul
%A TunĂ§, Cemil
%D 2024
%\ 04/01/2024
%V 10
%N 2
%P 317-329
%! Dynamics of Damped and Undamped Wave Natures of the Fractional Kraenkel-Manna-Merle System in Ferromagnetic Materials
%K The fractional Kraenkel-Manna-Merle system
%K M-Truncated derivative
%K Sardar sub-equation method
%K soliton solutions
%K nonlinear fractional differential equations
%R 10.22055/jacm.2023.45064.4307
%X 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).
%U https://jacm.scu.ac.ir/article_18685_0b82677a5f6a62b53ee88d1c521e6052.pdf