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. •Lie classical method is used to investigate the time fractional Harry-Dym equation.•The maximal Lie symmetry group of the equation under study is derived.•Optimal system of subgroups are determined and the optimization of the system is proved.•Reduced fractional ODEs and some exact solutions in explicit forms are presented.•The approach used here can also be applied to other nonlinear fractional PDEs.