Abstract
Here, two extended strategic algorithms, namely three-wave methods (Multi-waves interaction, rational solutions, interaction of rational solutions) and the method of Kudryashov expansion, are employed to build some new optical solitons to the space time-fractional Heisenberg systems for the ferromagnetic spin chains. The solutions obtained here contain the hyperbolic, rational, and trigonometric functions. The outcomes of this paper certainly show the impressive ability of the new expansion methods to deal with fractional nonlinear evolution equations in nonlinear science. Some 3D- and 2D-plots are provided for the simulations.