Document Type: Research Note
Department of Mathematics & Statistics, Banasthali University, Banasthali-304022, India
Department of Mathematics, University of Petroleum & Energy Studies, Dehradun, India.
Department of Mathematics, Faculty of Science, Ege University, Bornova - 35100, Turkey
In this paper, the approximate analytical solutions of Camassa-Holm, modied 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.