Complete Group Classifications and Symmetry Reductions of the Fractional Fifth-Order KdV Types of Equations

This paper is concerned with the fractional fifth-order KdV types of equations, the complete group classification is performed on the general fractional fifth-order partial differential equation (FPDE), which includes a lot of important fifth-order fractional differential equations and nonlinear evolution equations (NLEEs) as its special cases. In particular, all of the point symmetries of the fifth-order nonlinear evolution equation are presented with respect to the arbitrary parameters of the equation. In the sense of point symmetry, all of the vector fields of the equations are obtained. Then, the symmetry reductions are provided, and the exact analytic solutions to the general fifth-order KdV equations are investigated.