NUMERICAL SOLUTIONS OF INTEGRAL EQUATIONS USING SHIFTED FRACTIONAL VIETA-FIBONACCI POLYNOMIALS

In this paper, we propose a numerical technique to find approximate solutions of generalized Abel's integral equations, GAIEs, of the first and second kinds, based on the use of shifted fractional Vieta-Fibonacci polynomials. This possibility is created by establishing a relationship between th...

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Bibliographic Details
Published inTWMS journal of applied and engineering mathematics Vol. 15; no. 8
Main Authors Marasi, H.R, Hama, M.A
Format Journal Article
LanguageEnglish
Published Turkic World Mathematical Society 01.08.2025
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ISSN2146-1147

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Summary:In this paper, we propose a numerical technique to find approximate solutions of generalized Abel's integral equations, GAIEs, of the first and second kinds, based on the use of shifted fractional Vieta-Fibonacci polynomials. This possibility is created by establishing a relationship between the appearance of Abel's integral equations and the definition of fractional derivatives. The method reduces the numerical solutions of the Abel's integral equations to a system of algebraic equations. Convergence analysis and error bound of the proposed method are studied. The applicability and efficiency of the given methodology are demonstrated by a considerable number of examples. These examples show the remarkable superiority of our method. Keywords: Singular Volterra integral equation, Generalized Abel's integral equatio, Fractional calculus, Vieta-Fibonacci polynomial, Collocation method. AMS Subject Classification: 83-02, 99A00
ISSN:2146-1147