Lie symmetry analysis, invariant subspace method and conservation laws of the (3+1)-dimensional mixed fractional generalized Kadomtsev-Petviashvili equation

In this paper, we investigate the (3+1)-dimensional mixed fractional generalized Kadomtsev-Petviashvili equation (MFgKPE) with the time fractional Riemann-Liouville derivative which can describe the evolution of small amplitude nonlinear long waves with slow transverse coordinate dependence with time memory. Firstly, the Lie algebra admitted by MFgKPE is obtained. Then, the corresponding one-dimensional optimal system is provided. In addition, symmetry reductions are performed to construct the group invariant solutions. Specially, the polynomial solutions of the reduced equations are derived by invariant subspace method. Furthermore, the conservation laws for MFgKPE are set up through the new Noether's theorem. Finally, a visual demonstration of the three-dimensional and two-dimensional graphs of some of the obtained solutions are plottd and analysed.