We present the application of Lie group theory analysis with \(\zeta \)-Riemann–Liouville fractional derivative (\(\zeta \)-RLFD, for short) detailing the construction of infinitesimal prolongation to obtain Lie symmetries. In addition, it addresses the invariance condition without necessarily imposing that the lower limit of the fractional integral is fixed. We find an expression that expands the knowledge regarding the study of exact solutions for fractional differential equations. We apply the Leibniz-type rule for the derivative operator in question to build the prolongation. At last, we calculate the Lie symmetries of the generalized Burgers equation and fractional porous medium equation.

我们提出了李群理论分析与\(\zeta \) -Riemann-Liouville 分数阶导数（简称\(\zeta \) -RLFD）的应用，详细介绍了构造无穷小延拓以获得李对称性。此外，它解决了不变性条件，而不必强制要求分数积分的下限是固定的。我们找到了一个表达式，它扩展了有关分数阶微分方程精确解研究的知识。我们对所讨论的导数算子应用莱布尼茨型规则来构建延拓。最后，我们计算了广义Burgers方程和分数多孔介质方程的Lie对称性。