The optimal system, similarity reduction and group-invariant solutions to the Fractional Porous Medium equation and Fractional Dual Porous Medium equation

Abstract

In this paper, we developed the group analysis to the time Fractional Porous Medium Equation (FPME) and the time Fractional Dual Porous Medium Equation (FDPME). The symmetry groups and the corresponding optimal systems of these two equations are obtained. Based on the above results, similarity reductions are performed and some explicit group invariant solutions are constructed.