Approximate analytical solutions of fractional Benney–Lin equation by reduced differential transform method and the homotopy perturbation method

In this paper, the approximate analytical solutions of Benney–Lin equation with fractional time derivative are obtained with the help of a general framework of the reduced differential transform method (RDTM) and the homotopy perturbation method (HPM). RDTM technique does not require any discretization, linearization or small perturbations and therefore it reduces significantly the numerical computation. Comparing the methodology (RDTM) with some known technique (HPM) shows that the present approach is effective and powerful. The numerical calculations are carried out when the initial conditions in the form of periodic functions and the results are depicted through graphs. The eight different cases have studied and proved that the method is extremely effective due to its simplistic approach and performance.