Two-Dimensional Chebyshev Wavelet Method for Camassa-Holm Equation with Riesz Fractional Derivative Describing Propagation of Shallow Water Waves

Abstract

In this article, the authors present a new wavelet based method viz. Chebyshev wavelet method to compute the numerical solution of Riesz time-fractional Camassa-Holm equation. The approximate solutions of Riesz time-fractional Camassa-Holm equation thus obtained by two-dimensional Chebyshev wavelet method are compared with those obtained by analytical methods such as homotopy analysis method (HAM) and variational iteration method (VIM). The present scheme is quite simple, effective and appropriate for obtaining the numerical solution of the Riesz time-fractional Camassa-Holm equation.