Symmetries and exact solutions of the time fractional Harry-Dym equation with Riemann-Liouville derivative

In this paper, group analysis of the time fractional Harry-Dym equation with Riemann-Liouville derivative is performed. Its maximal symmetry group in Lie's sense and the corresponding optimal system of subgroups are determined. Similarity reductions of the equation under study are performed. As a result, the reduced fractional ordinary differential equations are deduced, and some group invariant solutions in explicit form are obtained as well.