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


Alam M. N., Rahim M. A., Hossain M. N., Tunç C.

Journal of Applied and Computational Mechanics, vol.10, no.2, pp.317-329, 2024 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 10 Issue: 2
  • Publication Date: 2024
  • Doi Number: 10.22055/jacm.2023.45064.4307
  • Journal Name: Journal of Applied and Computational Mechanics
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, Applied Science & Technology Source, Directory of Open Access Journals
  • Page Numbers: pp.317-329
  • Keywords: M-Truncated derivative, nonlinear fractional differential equations, Sardar sub-equation method, soliton solutions, The fractional Kraenkel-Manna-Merle system
  • Van Yüzüncü Yıl University Affiliated: Yes

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).