The current work is based on performing the non-classical and classical Lie group analysis for a system of nonlinear time-fractional Heisenberg equation. Here, we apply analysis of the Lie group symmetry as one of the powerful tools dealing with the large class of fractional order differential equations in the Riemann–Liouville (RL) sense. Indeed, classical and non-classical Lie symmetries group is used to similarity reduction of nonlinear time-fractional Heisenberg equation. Especially, based on the obtained Lie symmetry generators, we construct conservation laws for the classical and non-classical vector fields related to the Heisenberg time-fraction equation.
