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

In this paper, using the Lie group analysis method, we study the invariance properties of the time fractional generalized fifth-order KdV equation. It shows that this equation can be reduced to an equation which is related to the Erdélyi–Kober fractional derivative. Of course, this method can also be applied to other nonlinear fractional partial differential equations.

► Lie classical method is applied to investigate of time fractional generalized fifth-order KdV equation.
► The symmetry properties are derived.
► This equation can be transformed into a nonlinear ODE of fractional order.