Lie Symmetry Analysis, Power Series Solutions and Conservation Laws of (2+1)-Dimensional Time Fractional Modified Bogoyavlenskii–Schiff Equations

In this paper, Lie symmetry analysis method is applied to the (2+1)-dimensional time fractional modified Bogoyavlenskii–Schiff equations, which is an important model in physics. The one-dimensional optimal system composed by the obtained Lie symmetries is utilized to reduce the system of (2+1)-dimensional fractional partial differential equations with Riemann–Liouville fractional derivative to the system of (1+1)-dimensional fractional partial differential equations with Erdélyi–Kober fractional derivative. Then the power series method is applied to derive explicit power series solutions for the reduced system. In addition, the new conservation theorem and the generalization of Noether operators are developed to construct the conservation laws for the equations studied.