Exploring Novel Analytical Methods For Solving The Heisenberg Ferromagnetic-Type Fractional Akbota Equation: Comparative Graphical Analysis

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.