The functional variable method for solving the fractional Korteweg–de Vries equations and the coupled Korteweg–de Vries equations

This paper presents the exact solutions for the fractional Korteweg–de Vries equations and the coupled Korteweg–de Vries equations with time-fractional derivatives using the functional variable method. The fractional derivatives are described in the modified Riemann–Liouville derivative sense. It is demonstrated that the calculations involved in the functional variable method are extremely simple and straightforward and this method is very effective for handling nonlinear fractional equations.