Analytical solutions of conformable time, space, and time–space fractional KdV equations

Abstract

In this study, we consider the Korteweg–de Vries (KdV) equation for solitary waves in the domain ofconformable fractional calculus. By means of this fractional theory, we obtain exact solutions for time, space, andtime–space fractional KdV equations and demonstrate our results graphically according to the fractional order of therelated equations. Furthermore, we report that the fractional order in the solution of the time fractional KdV equationis associated with viscosity of the medium by comparing three-dimensional picture presentations of solutions of timefractional KdV and Burgers–KdV equations.