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

作者：Gupta P K^*; Singh M; Yildirim A

来源：Scientia Iranica, 2016, 23(1): 155-165.

• Partial differential equation
• Nonlinear fractional Camassa-Holm equation
• Fractional Brownian motion
• Homotopy perturbation method
• IVPs

In this paper, the approximate analytical solutions of Camassa-Holm, modified 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 effectiveness, validity, potentiality, and reliability of the method in reality. Comparing the methodology with the exact solution shows that the present approach is very effective 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.

• 出版日期2016
• 单位中国石油大学（北京）