In this paper, Lie symmetry analysis method is applied to time fractional Burgers equation, Korteweg-de Vries equation and generalized reaction-diffusion equation with delays, respectively. The Lie symmetries for fractional partial differential equations with delays (DFPDEs) are obtained, and the group classifications of the equations are established. The obtained group generators are used to reduce the DFPDEs to fractional ordinary differential equations with delays (DFODEs). Some exact solutions constructed for the DFODEs generate group-invariant solutions of the discussed DFPDEs.

中文翻译：

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时间分数阶 Burgers 方程、Korteweg-de Vries 方程和具有时滞的广义反应扩散方程的李对称性分析

本文分别将李对称分析方法应用于时间分数阶Burgers方程、Korteweg-de Vries方程和具有时滞的广义反应扩散方程。获得了具有时滞的分数阶偏微分方程 (DFPDE) 的李对称性，并建立了方程的群分类。获得的组生成器用于将 DFPDE 简化为具有延迟的分数阶常微分方程 (DFODE)。为 DFODE 构建的一些精确解生成所讨论的 DFPDE 的群不变解。