The fractional traveling wave solution of important Whitham–Broer–Kaup equations was
investigated by using the q-homotopy analysis transform method and natural decomposition
method. The Caputo definition of fractional derivatives is used to describe the fractional
operator. The obtained results, using the suggested methods are compared with each other
as well as with the exact results of the problems. The comparison shows the best agreement
of solutions with each other and with the exact solution as well. Moreover, the proposed …