Approximate nonclassical symmetries for the time-fractional KdV equations with the small parameter

In this paper, the Lie symmetry analysis is presented for the time-fractional KdV equation with the Riemann-Liouville derivative. We introduce a generalized approximate nonclassical method that is applied to differential equations with fractional order. In the sense of this symmetry, the vector fields of fractional KdV equation are obtained. The similarity reduction corresponding to the symmetries of the equation is constructed.

Keywords:

Approximate Lie symmetry analysis , Time-fractional KdV equation , Group-invariant solution