APPROXIMATE NONCLASSICAL SYMMETRIES FOR THE TIME-FRACTIONAL KDV EQUATIONS WITH SMALLPARAMETER

In this paper, the Lie symmetry analysis is presented for thetime-fractional KdV equation with the Riemann-Liouville derivative. Weintroduce a generalized approximate nonclassical method that is applied todi erential equations with fractional order. In the sense of this symmetry,the vector elds of fractional KdV equation are obtained. The similarityreduction corresponding to the symmetries of the equation is constructed.

Keywords:

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