Lie symmetry analysis to generalized fifth-order time-fractional KdV equation

Abstract

In present paper, the generalized fifth-order time-fractional Korteweg-de Vries (KdV) equation and the particular time-fractional Kaup-Kupershmidt equation are considered, a systematic investigation to derive Lie point symmetries of the equations are presented and compared. Each of them has been transformed into a nonlinear ordinary differential equation with a new independent variable are investigated. The derivative corresponding to time-fractional in the reduced formula is known as the Erdelyi-Kober fractional derivative.