Group classifications, optimal systems, symmetry reductions and conservation law of the generalized fractional porous medium equation

Abstract

This paper investigates the generalized fractional porous medium equations (GFPMEs) which are the generalizations of the dual porous medium equation with integer order derivative. The complete group classification of the equations in consideration are performed with respect to their arbitrary parameters. And all vector fields admitted by the GFPMEs are obtained with the help of Lie symmetry analysis. In addition, the corresponding optimal systems are provided and the group-invariant solutions to the GFPMEs are constructed by performing symmetry reductionsand the three-dimensional diagrams of the obtained group-invariant solutions are presented. Furthermore, the conservation law of one of the considered equations is established by means of new conservation theorem.