Its applications in many domains, along with its challenging analytical solution, have led to several studies of the Korteweg-de Vries (KdV) equation over the past decade. Due to difficulties or impossibility with the analytical solution to this equation, the paper presents a numerical solution using the Crank-Nicolson difference method. A study of the stability and solvency of this method has been undertaken. In this paper, we prove that the scheme is first order convergent in space and $\min \{ 2 - \nu ,r\nu \} $ order convergent in time, where $ r$ refers to a gradation parameter and $\nu$ represents the fractional derivative. The results are then presented in numerical applications, looking at how it compares with other sophisticated schemes in the literature. The main benefit of the proposed scheme is the efficiency with regard to accuracy as compared to other available schemes.
