This paper investigates the generalized fractional porous medium equations (GFPMEs) which are the generalizations of the dual porous medium equation with integer order derivative. The complete group classification of the equations in consideration are performed with respect to their arbitrary parameters. And all vector fields admitted by the GFPMEs are obtained with the help of Lie symmetry analysis. In addition, the corresponding optimal systems are provided and the group-invariant solutions to the GFPMEs are constructed by performing symmetry reductionsand the three-dimensional diagrams of the obtained group-invariant solutions are presented. Furthermore, the conservation law of one of the considered equations is established by means of new conservation theorem.

本文研究了广义分数多孔介质方程（GFPMEs），它是具有整数阶导数的对偶多孔介质方程的推广。所考虑的方程的完整组分类是相对于它们的任意参数执行的。并且 GFPMEs 承认的所有矢量场都是在李对称分析的帮助下获得的。此外，给出了相应的最优系统，并通过对称约简构造了GFPME的群不变解，并给出了得到的群不变解的三维图。此外，所考虑的方程之一的守恒定律是通过新的守恒定理建立的。