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

Issue title: Theory and Applications of Fractional Fourier Transform and its Variants

Guest editors: Yudong Zhang, Xiao-Jun Yang, Carlo Cattani, Zhengchao Dong, Ti-Fei Yuan and Liang-Xiu Han

Article type: Research Article

Authors: Gupta, A.K. | Saha Ray, S.^*

Affiliations: National Institute of Technology, Department of Mathematics, Rourkela-769008, Odisha, India. [email protected]

Correspondence: [*] Address for correspondence: National Institute of Technology, Department of Mathematics, Rourkela-769008, Odisha, India

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.

Keywords: Camassa-Holm equation, Chebyshev wavelet method, Riesz fractional derivative, Left Riemann-Liouville derivative, Right Riemann-Liouville derivative

DOI: 10.3233/FI-2017-1480

Journal: Fundamenta Informaticae, vol. 151, no. 1-4, pp. 77-89, 2017