Exact solitary solutions for variants of the KdV equations with fractional time derivatives

In this paper, the homotopy perturbation method is implemented to construct solitary solutions for variants of the KdV 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. Two models are investigated and the obtained results reveal that the method is very effective and convenient for constructing solitary solutions for nonlinear problems with fractional time derivatives.