A Jacobi spectral method for calculating fractional derivative based on mollification regularization

Article type: Research Article

Authors: Zhang, Wen^{a; *} | Wu, Changxing^a | Ruan, Zhousheng^a | Qiu, Shufang^{a; b}

Affiliations: [a] School of Science, East China University of Technology, Nanchang, Jiangxi, 330013, P.R. China | [b] Department of Basic Courses, Guangzhou Maritime University, Guangzhou, Guangdong, 510725, P.R. China

Correspondence: [*] Corresponding author. E-mail: zhangwenmath@126.com.

Abstract: In this article, we construct a Jacobi spectral collocation scheme to approximate the Caputo fractional derivative based on Jacobi–Gauss quadrature. The convergence analysis is provided in anisotropic Jacobi-weighted Sobolev spaces. Furthermore, the convergence rate is presented for solving Caputo fractional derivative with noisy data by invoking the mollification regularization method. Lastly, numerical examples illustrate the effectiveness and stability of the proposed method.

Keywords: Fractional derivative, Jacobi collocation, mollification, Gaussian quadrature

DOI: 10.3233/ASY-231869

Journal: Asymptotic Analysis, vol. 136, no. 1, pp. 61-77, 2024