In this work, we investigate invariance analysis, conservation laws, and exact power series solutions of time fractional generalized Drinfeld–Sokolov systems (GDSS) using Lie group analysis. Using Lie point symmetries and the Erdelyi–Kober (EK) fractional differential operator, the time fractional GDSS equation is reduced to a nonlinear ordinary differential equation (ODE) of fractional order. Moreover, we have constructed conservation laws for time fractional GDSS and obtained explicit power series solutions of the reduced nonlinear ODEs that converge. Lastly, some figures are presented for explicit solutions.

中文翻译：

---

分数次广义Drinfeld-Sokolov系统的Lie对称性分析，守恒律，幂级数解和收敛性分析

在这项工作中，我们使用李群分析研究时间分数广义Drinfeld-Sokolov系统（GDSS）的不变性分析，守恒定律和精确幂级数解。使用Lie点对称性和Erdelyi–Kober（EK）分数阶微分算子，将时间分数GDSS方程简化为分数阶的非线性常微分方程（ODE）。此外，我们构造了时间分数GDSS的守恒律，并获得了收敛的简化非线性ODE的显式幂级数解。最后，给出了一些数字，用于明确的解决方案。