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.

In this paper, we have presented the applicability of the first integral method for constructing exact solutions of (2+1)-dimensional Jaulent–Miodek equations. The first integral method is a powerful and effective method for solving nonlinear partial differential equations which can be applied to nonintegrable as well as integrable equations. The present paper confirms the significant features of the method employed and exact kink and soliton solutions are constructed through the established first integrals.