Generalized solitary wave solutions to the time fractional generalized Hirota-Satsuma coupled KdV via new definition for wave transformation

In this paper, the (G′/G)-expansion method has been applied to explore new solitary wave solutions for the time fractional generalized Hirota-Satsuma coupled KdV (FGHSC KdV) system. The fractional derivative is described with the use of conformable derivative. The results show that this method is a very useful and effective mathematical tool for solving nonlinear conformable fractional equations arising in mathematical physics. As a result, this method can also be applied to other nonlinear conformable fractional differential equations.