Fractal and Fractional (Jul 2023)

The Analytical Solutions to the Fractional Kraenkel–Manna–Merle System in Ferromagnetic Materials

  • Mohammad Alshammari,
  • Amjad E. Hamza,
  • Clemente Cesarano,
  • Elkhateeb S. Aly,
  • Wael W. Mohammed

DOI
https://doi.org/10.3390/fractalfract7070523
Journal volume & issue
Vol. 7, no. 7
p. 523

Abstract

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In this article, we examine the Kraenkel–Manna–Merle system (KMMS) with an M-truncated derivative (MTD). Our goal is to obtain rational, hyperbolic, and trigonometric solutions by using the F-expansion technique with the Riccati equation. To our knowledge, no one has studied the exact solutions to the KMMS in the presence/absence of a damping effect with an M-truncated derivative, using the F-expansion technique. The magnetic field propagation in a zero-conductivity ferromagnet is described by the KMMS; hence, solutions to this equation may provide light on several fascinating scientific phenomena. We use MATLAB to display figures in a variety of 3D and 2D formats to demonstrate the influence of the M-truncated derivative on the exact solutions to the KMMS.

Keywords