Comparison between solutions of a two-dimensional time-fractional diffusion-reaction equation through Lie symmetries

In this paper, exact and numerical solutions of two dimensional time-fractional diffusion-reaction equation involving the Riemann-Liouville derivative are determined, by applying a procedure that combines the Lie symmetry analysis with the numerical methods. Two new reduced fractional differential equations are obtained by using the Lie symmetry theory. Applying only one Lie transformation, we get a new time-fractional partial differential equation and, applying a further Lie transformation, we get an ordinary differential equation. Numerical solutions of the reduced differential equations are computed separately by implicit numerical methods. A comparative study between numerical solutions is performed.