Two effective approaches for solving fractional generalized Hirota-Satsuma coupled KdV system arising in interaction of long waves

•Summary the sub-equation method and power series method were successfully utilized to establish a series of new exact traveling wave solutions for the fractional generalized Hirota-Satsuma coupled KdV system.•As a result, a series of new traveling wave solutions for the fractional generalized Hirota-Satsuma coupled KdV system were formally extracted. The performance of these methods are reliable, effective and computerized mathematical tool to handle nonlinear evolution equations in the field of mathematical physics and applied sciences. 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.