The time-fractional (2+1)-dimensional Heisenberg ferromagnetic spin chain equation: its Lie symmetries, exact solutions and conservation laws

Abstract In this paper, the Lie symmetry analysis method is applied to the (2+1)-dimensional time-fractional Heisenberg ferromagnetic spin chain equation. We obtain all the Lie symmetries admitted by the governing equation and reduce the corresponding (2+1)-dimensional fractional partial differential equations with the Riemann–Liouville fractional derivative to (1+1)-dimensional counterparts with the Erdélyi–Kober fractional derivative. Then, we obtain the power series solutions of the reduced equations, prove their convergence and analyze their dynamic behavior graphically. In addition, the conservation laws for all the obtained Lie symmetries are constructed using the new conservation theorem and the generalization of Noether operators.