Solitary solutions for the nonlinear dispersive K(m,n) equations with fractional time derivatives

In this Letter, the homotopy perturbation method is implemented to construct exact solitary solutions for the nonlinear dispersive K(m,n) equations with fractional time derivatives. In this scheme the solution takes the form of a convergent series with easily computable components. The chosen initial solution or trial function plays a major role in changing the physical structure of the solution. Three special cases, K(2,2), K(3,3) and K(n,n), with factional time derivatives in the sense of Caputo are investigated and the obtained results reveal that the method is very effective and convenient for constructing solitary solutions for nonlinear fractional dispersive equations.