In this article, two different methods, namely sub-equation method and residual power series method, have been used to obtain new exact and approximate solutions of the generalized Hirota-Satsuma system of equations, which is a coupled KdV model. The fractional derivative is taken in the conformable sense. Each of the obtained exact solutions were checked by substituting them into the corresponding system with the help of Maple symbolic computation package. The results indicate that both methods are easy to implement, effective and reliable. They are therefore ready to apply for various partial fractional differential equations.
