Abstract
This study employs advanced mathematical techniques to investigate exact solutions for the fractional (2+1)-dimensional Heisenberg ferromagnetic spin chain (HFSC) equation. Novel complex transformations-based on the generalized conformable derivative, exponential functions, arctanh, and arctan-are used to reduce the partial differential equation to an ordinary one. Three analytical methods are applied to obtain solutions: the modified Kudryashov method, the improved Bernoulli subequation function method (IBSEFM), and the modified extended direct algebraic method (mEDAM). These methods yield kink-wave, hyperbolic, trigonometric, and periodic wave solutions, which are validated through 2D, 3D, and contour plots for specific parameter choices. The main objective of this study is to derive exact soliton solutions of the Heisenberg spin chain equation using generalized conformable derivatives through multiple analytical methods. A sensitivity analysis is also performed to study how small changes in initial conditions affect the system's behavior. These findings may contribute to future data storage technologies and magnetic memory developments. The proposed approaches demonstrate efficiency in solving nonlinear fractional equations and have potential applications in shallow water waves, fluid dynamics, quantum mechanics, lattice vibrations in condensed matter, shock wave propagation in plasma, and phase transitions in ferromagnetic materials. The study highlights the effectiveness and reliability of the employed techniques.