EXPLORING NOVEL ANALYTICAL METHODS FOR SOLVING THE HEISENBERG FERROMAGNETIC-TYPE FRACTIONAL AKBOTA EQUATION: COMPARATIVE GRAPHICAL ANALYSIS

Dean Chou, Ifrah Iqbal (), A. F. Aljohani (), Saad Althobaiti () and Hamood Ur Rehman
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Dean Chou: Department of Biomedical Engineering, National Cheng Kung, Tainan 701401, Taiwan2Miin Wu School of Computing, National Cheng Kung, Tainan 701401, Taiwan3Academy of Innovative Semiconductor and Sustainable Manufacturing, National Cheng Kung, Tainan 701401, Taiwan4National Center for High-Performance Computing, Hsinchu 300092, Taiwan
Ifrah Iqbal: Department of Mathematics, University of Okara, Okara, Pakistan
A. F. Aljohani: Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk, Saudi Arabia
Saad Althobaiti: Department of Science and Technology, University College Ranyah, Taif University, Ranyah 21975, Saudi Arabia
Hamood Ur Rehman: Department of Mathematics, University of Okara, Okara, Pakistan8Center for Theoretical Physics, Khazar University, 41 Mehseti Street, Baku, AZ1096, Azerbaijan

FRACTALS (fractals), 2025, vol. 33, issue 08, 1-14

Abstract: Fractional-order models have demonstrated greater effectiveness in explaining long-range interactions and non-locality effects in systems compared to classical models. Additionally, these models provide a more accurate representation of memory effects within the system, which are crucial for a detailed prediction of soliton propagation characteristics. In this research, we focus on the Akbota equation which is an integrable equation of the Heisenberg ferromagnetic type that plays significant role in analyzing curves and surface geometry, with important applications in the fields of magnetics and optics. We investigate novel analytical soliton solutions for the fractional nonlinear (1+1)-dimensional Akbota equation through the M-truncated fractional derivative framework. Our approach employs advanced techniques, including the 1 φ(η), φ′(η) φ(η) , method, the modified extended tanh method (METM), and the generalized Arnous method (GAM). These methods enable us to derive different soliton solutions in the form of singular, periodic-singular, dark, bright, and combined dark-singular solutions. We also present comprehensive graphs that visualize the solutions of the Akbota equation across different scenarios to illustrate their dynamic behavior under varying conditions. We also compare our solutions with the existing literature to highlight the novelty of our findings through a detailed investigation of solutions obtained by using different parameter values. This application of METM, 1 φ(η), φ′(η) φ(η) and GAM to the fractional Akbota equation is unprecedented in the current context and underscores the significance of our contributions to the field of nonlinear dynamics.

Keywords: 1 φ(η); φ′(η) φ(η) Method; Modified Extended Tanh Method (METM); M-Truncated Fractional Derivative; Generalized Arnous Method (GAM); Heisenberg Equations (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X25401577

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