Abstract
This article introduces the fractional (2+1)-dimensional evolution model portraying the transmission of nonlinear spin dynamics in Heisenberg ferromagnetic spin chains with bilinear and anisotropic interactions in the semiclassical limit. Fractional derivatives stand out in modeling problems involving the concepts of non-locality and memory effect, that are not well explained by the integer-order calculus. New extended generalized Kudryashov method is employed to construct traveling wave solutions of governing equation. These solutions such as dark, singular solitons, solitary waves and singular solitary waves arise with constraint conditions and exhibit distinct physical significance. Since magnetic soliton has been classified as one of the fascinating groups of nonlinear excitations expressing spin dynamics in semiclassical continuum Heisenberg systems. 3D and 2D graphs for suitable parametric values are provided to interpret the dynamics of soliton profiles. Also, a comparative analysis is shown among Beta and Atangana-Baleanu fractional derivatives. Our results assert that this scheme is reliable and efficient gadget for extracting the soliton solutions of different nonlinear evolution equations appearing in mathematical sciences.