Traveling Wave Solutions to Riesz Time Fractional Camassa–Holm Equation in Modeling for Shallow Water Waves

Abstract

In the present paper, we construct the analytical exact solutions of a nonlinear evolution equation in mathematical physics, viz., Riesz timefractional Camassa–Holm (CH) equation by modified homotopy analysis method (MHAM). As a result, new types of solutions are obtained. Then, we analyze the results by numerical simulations, which demonstrate the simplicity and effectiveness of the present method. The main aim of this paper is to employ a new approach, which enables us successful and efficient derivation of the analytical solutions for the Riesz timefractional CH equation.