Approximate analytical solution of the time-fractional Camassa-Holm, modified Camassa-Holm and Degasperis-Procesi equations by Homotopy perturbation method

In this paper, the approximate analytical solutions of Camassa-Holm, modified Camassa-Holm and Degasperis-Procesi equationswith fractional time derivative are obtained with the help of approximate analytical method of nonlinear problem called the Homotopy Perturbation Method (HPM). By using initial condition, the explicit solution of the equation has been derived which demonstrate the effectiveness, validity, potentiality and reliability of the method in reality. Comparing the methodology with exact solution shows that the present approach is very effective and powerful. The numerical calculations are carried out when the initial condition in the form of exponential and transcendental functions and the results are depicted through graphs.