141
Views
2
CrossRef citations to date
0
Altmetric
Articles

Fractional Chebyshev cardinal wavelets: application for fractional quadratic integro-differential equations

, &
Pages 479-496 | Received 08 May 2021, Accepted 29 Aug 2022, Published online: 16 Sep 2022
 

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.

2022 Mathematical Subject Classification:

Disclosure statement

No potential conflict of interest was reported by the author(s).

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.