A Semianalytical Approach for the Solution of Nonlinear Modified Camassa–Holm Equation with Fractional Order

Jiahua Fang, Muhammad Nadeem, Hanan A. Wahash
2022 Journal of Mathematics  
This paper presents the approximate solution of the nonlinear acoustic wave propagation model is known as the modified Camassa–Holm (mCH) equation with the Caputo fractional derivative. We examine this study utilizing the Laplace transform (ℒT) coupled with the homotopy perturbation method (HPM) to construct the strategy of the Laplace transform homotopy perturbation method (ℒ T-HPM). Since the Laplace transform is suitable only for a linear differential equation, therefore ℒ T-HPM is the
more » ... le approach to decompose the nonlinear problems. This scheme produces an iterative formula for finding the approximate solution of illustrated problems that leads to a convergent series without any small perturbation and restriction. Graphical results demonstrate that ℒ T-HPM is simple, straightforward, and suitable for other nonlinear problems of fractional order in science and engineering.
doi:10.1155/2022/5665766 doaj:0e0efaf0d4bf48f1aba32ae1391842e0 fatcat:u6jzhqitbndlbnkuprcnihcpiu