Journal of Applied and Computational Mechanics

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

Document Type : Research Paper

Authors

1 Department of Mathematics, Pabna University of Science and Technology, Pabna, 6600, Bangladesh

2 Department of Computer Science and Engineering, Pabna University of Science and Technology, Pabna, 6600, Bangladesh

3 Department of Electrical, Electronic and Communication Engineering, Pabna University of Science and Technology, Pabna, 6600, Bangladesh

4 Department of Mathematics, Faculty of Sciences, Van Yuzuncu Yil University, 65080, Van, Turkey

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 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).

Keywords

Main Subjects

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Journal of Applied and Computational Mechanics
Volume 10, Issue 2
April 2024
Pages 317-329