Exact solutions for the fractional differential equations by using the first integral method

[摘要] In this paper, we apply the first integral method to study the solutions of the nonlinear fractional modified Benjamin-Bona-Mahony equation, the nonlinear fractional modified Zakharov-Kuznetsov equation and the nonlinear fractional Whitham-Broer-Kaup-Like systems. This method is based on the ring theory of commutative algebra. The results obtained by the proposed method show that the approach is effective and general. This approach can also be applied to other nonlinear fractional differential equations, which are arising in the theory of solitons and other areas.

[关键词] fractional derivative;first integral method;modified Benjamin-Bona-Mahon equation;modified Zakharov-Kuznetsov equation;Whitham-Broer-Kaup-Like system