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

ABSTRACT

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.

Acknowledgements

The authors appreciate the constructive remarks and suggestions of the anonymous referees that helped to improve the paper. We gratefully acknowledge to the Universidad Autónoma de la Ciudad de México for supporting this research work.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

José Francisco Gómez Aguilar acknowledges the support provided by CONACyT: Cátedras CONACyT para jóvenes investigadores 2014. Huitzilín Yépez Martínez and José Francisco Gómez Aguilar acknowledges the support provided by SNI-CONACyT.