  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.
