Exact and numerical solutions of two-dimensional time-fractional diffusion–reaction equations through the Lie symmetries

In this paper, a two-dimensional time-fractional diffusion-reaction equation involving the Riemann–Liouville derivative is considered. Exact and numerical solutions are obtained by applying a procedure that combines the Lie symmetry analysis with the numerical methods. Lie symmetries are determined; then through the Lie transformations, the target equation is reduced into a new one-dimensional time-fractional differential equation. By solving the reduced fractional partial differential equation, exact and numerical solutions are found. The numerical solutions are determined by introducing the Caputo definition fractional derivative and by using an implicit classical numerical method. Comparisons between the numerical and exact solutions are performed.