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

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 (Script capital LT) coupled with the homotopy perturbation method (HPM) to construct the strategy of the Laplace transform homotopy perturbation method (Script capital LT-HPM). Since the Laplace transform is suitable only for a linear differential equation, therefore Script capital LT-HPM is the suitable 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 Script capital LT-HPM is simple, straightforward, and suitable for other nonlinear problems of fractional order in science and engineering.

Automated summary

This paper presents an approximate solution for the nonlinear acoustic wave propagation model known as the modified Camassa-Holm equation with Caputo fractional derivative. The Laplace transform combined with the homotopy perturbation method is used to construct the strategy of Laplace transform homotopy perturbation method. This method is suitable for decomposing nonlinear problems and generates a convergent series without requiring small perturbation or restriction. Graphical results demonstrate that this method is simple, direct, and applicable to other nonlinear fractional order problems in science and engineering.