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

Document Type: Research Note

Authors

1 Department of Mathematics & Statistics, Banasthali University, Banasthali-304022, India

2 Department of Mathematics, University of Petroleum & Energy Studies, Dehradun, India.

3 Department of Mathematics, Faculty of Science, Ege University, Bornova - 35100, Turkey

Abstract

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 e ectiveness, validity, potentiality, and reliability of the method in reality. Comparing the methodology with the exact solution
shows that the present approach is very e ective 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.

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