A Novel Vieta–Fibonacci Projection Method for Solving a System of Fractional Integrodifferential Equations

Abdelkader Moumen, Abdelaziz Mennouni () and Mohamed Bouye
Additional contact information
Abdelkader Moumen: Department of Mathematics, Faculty of Sciences, University of Ha’il, Ha’il 55425, Saudi Arabia
Abdelaziz Mennouni: Department of Mathematics, LTM, University of Batna 2, Mostefa Ben Boulaïd, Fesdis, Batna 05078, Algeria
Mohamed Bouye: Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia

Mathematics, 2023, vol. 11, issue 18, 1-14

Abstract: In this paper, a new approach for numerically solving the system of fractional integrodifferential equations is devised. To approximate the issue, we employ Vieta–Fibonacci polynomials as basis functions and derive the projection method for Caputo fractional order for the first time. An efficient transformation reduces the problem to a system of two independent equations. Solving two algebraic equations yields an approximate solution to the problem. The proposed method’s efficiency and accuracy are validated. We demonstrate the existence of the solution to the approximate problem and conduct an error analysis. Numerical tests reinforce the interpretations of the theory.

Keywords: integrodifferential equations; system; fractional; Vieta–Fibonacci polynomials; projection method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/18/3985/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/18/3985/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:18:p:3985-:d:1243418

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().