Fractional sub-equation method for Hirota-Satsuma-coupled KdV equation and coupled mKdV equation using the Atangana's conformable derivative

摘要

In this paper, we present the exact solutions obtained for the space-time conformable generalized Hirota-Satsuma-coupled KdV equation and coupled mKdV equation using the Atangana's conformable derivative. The conformable sub-equation method is applied to obtain the solutions; the solutions obtained are compared with the extended tanh-function method for the special case when the fractional order takes the integer order. The analytical solutions show that the conformable sub-equation method is very effective for the conformable-coupled KdV and mKdV equations.