A spectral collocation method for solving fractional KdV and KdV-Burgers equations with non-singular kernel derivatives

The purpose of this paper is to investigate the spectral collocation method with help of Chebyshev polynomials. We consider the space fractional Korteweg-de Vries and the space fractional Korteweg-de Vries-Burgers equations based on the Caputo-Fabrizio fractional derivative. The proposed method reduces the models under study to a set of ordinary differential equations and then solves the system via the finite difference method. To the best our knowledge this is the first work which studies the Caputo-Fabrizio space fractional derivative for the proposed equations. The results were validated in the case of the classic differential equations in comparison with the exact solution and the calculation of the absolute error, and in the case of fractional differential equations, the results were verified by calculating the residual error function. In both cases, the results are very accurate and effective. The presented method is easy and accurate, and can be applied to many fractional systems.