Lie symmetry analysis of (2+1)-dimensional time fractional Kadomtsev-Petviashvili equation

TL;DR

This paper applies Lie symmetry analysis to a (2+1)-dimensional time fractional KP equation, deriving symmetries, reducing the equation, finding solutions, and developing conservation laws.

Contribution

It introduces a comprehensive symmetry analysis for the fractional KP equation, including reductions, solutions, and conservation laws, which is novel for this type of fractional PDE.

Findings

All Lie symmetries of the fractional KP equation are obtained.

The equation is reduced to lower-dimensional fractional PDEs with exact solutions.

New conservation laws and generalized Noether operators are established.

Abstract

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.