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

Author

Listed:
  • Abdelkader Moumen

    (Department of Mathematics, Faculty of Sciences, University of Ha’il, Ha’il 55425, Saudi Arabia
    These authors contributed equally to this work.)

  • Abdelaziz Mennouni

    (Department of Mathematics, LTM, University of Batna 2, Mostefa Ben Boulaïd, Fesdis, Batna 05078, Algeria
    These authors contributed equally to this work.)

  • Mohamed Bouye

    (Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Abdelkader Moumen & Abdelaziz Mennouni & Mohamed Bouye, 2023. "A Novel Vieta–Fibonacci Projection Method for Solving a System of Fractional Integrodifferential Equations," Mathematics, MDPI, vol. 11(18), pages 1-14, September.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:18:p:3985-:d:1243418
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    References listed on IDEAS

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    1. Ahmad, Bashir & K. Ntouyas, Sotiris, 2015. "Existence results for a coupled system of Caputo type sequential fractional differential equations with nonlocal integral boundary conditions," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 615-622.
    2. Saeed Althubiti & Abdelaziz Mennouni, 2022. "A Novel Projection Method for Cauchy-Type Systems of Singular Integro-Differential Equations," Mathematics, MDPI, vol. 10(15), pages 1-11, July.
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