Analytic investigation of the (2+1)-dimensional Heisenberg ferromagnetic spin chain equation with M-fractional derivative

In this study, we examine the Heisenberg ferromagnetic spin chain equation in complex form in (2+1) dimensions, which is closely related to ferromagnetic materials and is used in spin wave dynamics modeling. To better interpret the model physically, we considered M-truncated time fractional derivative operator and used the generalized exponential rational function and extended trial equation methods to reveal the exact solution forms. These exact solution forms are presented in hyperbolic, trigonometric, and rational forms. We give 2D and 3D numerical simulations of exact solution profiles. The importance of fractional calculus in extending nonlinear theory is emphasized.