Time-fractional inhomogeneous nonlinear diffusion equation: Symmetries, conservation laws, invariant subspaces, and exact solutions

In this paper, a class of time-fractional inhomogeneous nonlinear diffusion equation (tFINDE) with Riemann-Liouville fractional derivative is studied. All point symmetries admitted by this equation are derived. The optimal system of one-dimensional subal-gebras is classified to perform the symmetry reductions. It is shown that the tFINDE can be reduced to fractional ordinary differential equations (FODEs), including Erdelyi- Kober fractional derivatives. As the results, some explicit group-invariant solutions are obtained. Through nonlinear self-adjointness, all conservation laws admitted by tFINDE arising from these point symmetry groups are listed. The method of invariant subspace is also applied to reduce the tFINDE to a two-dimensional dynamical system (DS). The admitted point symmetries of DS are used to derive the exact solutions of DS, which determine the exact solutions of the original tFINDE.