Abstract: We considered  the existence of travelling wave solutions of a class of space- time Whitham-Broer-Kaup (WBK) equations with modified RiemannLiouville fractional derivative. First, we turned the WBK equations into the ordinary differential equations, and then got analytical expressions of some travelling wave solutions of this equations by using the first integral method.

Key words: space-time fractional WBK equation, modified Riemann-Liouville fractional derivative, travelling wave solution, first integral method