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

## TL;DR

This paper applies group analysis to fractional porous medium equations, deriving symmetry groups, optimal systems, and explicit solutions, advancing understanding of these fractional PDEs.

## Contribution

It introduces symmetry analysis and explicit solutions for fractional porous medium and dual equations, a novel approach in this context.

## Key findings

- Symmetry groups and optimal systems identified for both equations.
- Explicit group-invariant solutions constructed.
- Enhanced understanding of fractional porous medium equations.

## 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.