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In this paper, Lie group analysis is developed to investigate the time-fractional Porous Medium equation. The symmetry group and the corresponding optimal system are obtained. Then, the similarity reductions are performed to construct some explicit group-invariant solutions. In addition, the conservation laws are derived by applying the new conservation theorem. Furthermore, some separation variable type solutions are obtained with the help of the homogenous balanced principle.

Lie symmetry analysis, conservation laws and separation variable type solutions of the time-fractional porous medium equation