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An Effective Numerical Approach for Fractional Integro-Differential Systems Using Shifted Airfoil Polynomials

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  • Saeed Althubiti

Abstract

In this paper, we propose a projection method that utilizes shifted airfoil polynomials to solve systems of weakly singular fractional integro-differential equations (FIDEs). The proposed approach converts the original system into two linear algebraic systems, facilitating efficient numerical solutions. We establish the existence of solutions and provide a rigorous error analysis within the weighted Hilbert space LÏ‘20,1. Several numerical examples are presented to support the theoretical findings and to demonstrate the superiority of the method compared to classical polynomial bases.

Suggested Citation

  • Saeed Althubiti, 2026. "An Effective Numerical Approach for Fractional Integro-Differential Systems Using Shifted Airfoil Polynomials," Journal of Mathematics, Hindawi, vol. 2026, pages 1-13, July.
    • Handle: RePEc:hin:jjmath:5771120
    DOI: 10.1155/jom/5771120
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