Abstract
In this paper, we studied the generalized space and time fractional Korteweg-de Vries (KdV) equation in the sense of the Riemann-Liouville fractional derivative. Initially, the symmetry of this considered equation through the symmetry analysis method was obtained. Next, a one-parameter Lie group of point transformation was yielded. Then, this considered fractional model can be translated into an ordinary differential equation of fractional order via the Erdelyi-Kober fractional differential operator and the Erdelyi-Kober fractional integral operator. Finally, with the help of the nonlinear self-adjointness, conservation laws of the generalized space and time fractional KdV equation can be found. This approach can provide us with a new scheme for studying space and time differential equations of fractional derivative.