A Novel Orthogonal TU¯ Chebyshev Polynomial Basis for High-Accuracy Solution of Fractional Integro-Differential Equations

Samiye Akhlaghi, Maryam Bahmanpour and Majid Tavassoli Kajani

Journal of Mathematics, 2026, vol. 2026, 1-11

Abstract: The main question addressed in this study is whether a newly constructed orthogonal basis, which is a combination of first- and second-kind Chebyshev polynomials, can provide a more accurate and efficient numerical method for solving fractional integro-differential equations. To this end, a new family of normalized orthogonal polynomials, called Chebyshev polynomials TU¯, is introduced. This basis is constructed by normalizing the first- and second-kind Chebyshev polynomials, forming their structural sum, and applying a weighted Gram–Schmidt process, yielding a normalized orthogonal system with enhanced approximation flexibility. Based on the TU¯ basis, the main problem is transformed into a system of algebraic equations using the collocation method, reducing computational complexity. A rigorous error analysis ensures the convergence of the method and validates its reliability. Numerical results demonstrate that the proposed method achieves higher accuracy and faster convergence compared with classical Chebyshev-based approaches, confirming the effectiveness of the TU¯ basis in solving fractional integro-differential problems

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:9111094

DOI: 10.1155/jom/9111094

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