In this paper, Lie symmetry analysis method is applied to the (2+1)-dimensional time fractional Kadomtsev-Petviashvili (KP) equation with the mixed derivative of Riemann-Liouville time-fractional derivative and integer-order $x$-derivative. We obtained all the Lie symmetries admitted by the KP equation and used them to reduce the (2+1)-dimensional fractional partial differential equation with Riemann-Liouville fractional derivative to some (1+1)-dimensional fractional partial differential equations with Erd\'{e}lyi-Kober fractional derivative or Riemann-Liouville fractional derivative, thereby getting some exact solutions of the reduced equations. In addition, the new conservation theorem and the generalization of Noether operators are developed to construct the conservation laws for the equation studied.

翻译：本文应用Lie对称性分析方法研究具有Riemann-Liouville时间分数阶导数与整数阶$x$方向导数混合导数的(2+1)维时间分数阶Kadomtsev-Petviashvili (KP)方程。我们获得了该KP方程所允许的所有Lie对称性，并利用这些对称性将具有Riemann-Liouville分数阶导数的(2+1)维分数阶偏微分方程约化为若干具有Erdélyi-Kober分数阶导数或Riemann-Liouville分数阶导数的(1+1)维分数阶偏微分方程，从而得到这些约化方程的一些精确解。此外，我们还发展了新的守恒定理和Noether算子的推广形式，用于构造所研究方程的守恒律。