Fractional Chebyshev cardinal wavelets: application for fractional quadratic integro-differential equations. Issue 3 (4th March 2023)

• Record Type: Journal Article
• Authors: Heydari, M. H.; Razzaghi, M.; Cattani, C.
• Is Part Of: International journal of computer mathematics. Volume 100:Issue 3(2023)
• Page Start: 479
• Page End: 496
• Publication Date: 2023-03-04
• Subjects: Fractional Chebyshev cardinal wavelets -- quadratic integro-differential equations -- operational matrices -- error analysis; 26A33; Computers -- Periodicals; Numerical analysis -- Periodicals; Automation -- Periodicals; 004.0151
• DOI: 10.1080/00207160.2022.2122052
• Languages: English
• ISSNs: 0020-7160

Abstract

Abstract : This paper introduces a new set of the basis functions called the fractional Chebyshev cardinal wavelets and details their properties. These wavelets have a greater degree of freedom than the classical Chebyshev cardinal wavelets. Moreover, they retain the cardinality and the spectral accuracy of these wavelets. The fractional derivative and integral matrices of these fractional basis functions are obtained exactly in the explicit forms. In this study, we aim to devise an efficient and powerful approximation method using these new basis functions. Then, we employ them for a new category of nonlinear fractional quadratic integro-differential equations. By employing their fractional integral matrix and their cardinality, the problem under study is transformed into solving a nonlinear system of algebraic equations. The error analysis of the presented technique is first investigated theoretically and then computational efficiency is examined for two numerical examples.