Symmetry Analysis and Conservation Laws for a Time-Fractional Generalized Porous Media Equation

The symmetry group method is applied to study a class of time-fractional generalized porous media equations with Riemann-Liouville fractional derivatives. All point symmetry groups and the corresponding optimal subgroups are determined. Then, the similarity reduction is performed to the given equation and some explicit solutions are derived. The asymptotic behaviours for the solutions are also discussed. Through the concept of nonlinear self-adjointness, the conservation laws arising from the admitted point symmetries are listed.