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.

中文翻译：

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时间分数多孔介质方程的李对称分析、守恒定律和分离变量型解

在本文中，开发了李群分析来研究时间分数多孔介质方程。得到对称群和相应的最优系统。然后，执行相似性降低以构造一些显式的组不变解。此外，通过应用新的守恒定理推导出守恒定律。此外，借助同质平衡原理，得到了一些分离变量类型的解。