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

In this paper, the approximate analytical solutions of Camassa-Holm, modied Camassa-Holm, and Degasperis-Procesi equations with 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 demonstrates the eectiveness, validity, potentiality, and reliability of the method in reality. Comparing the methodology with the exact solution shows that the present approach is very eective and powerful. The numerical calculations are carried out when the initial condition is in the form of exponential and transcendental functions; the results are depicted through graphs.