TY - JOUR T1 - Efficient Computational Techniques for Fractional Order Delay-Integro Differential Equations TT - Kesirli Mertebeden Gecikmeli-İntegro Diferansiyel Denklemler için Etkili Yöntemler AU - Akarsu, Eda AU - Gülsu, Mustafa PY - 2025 DA - April Y2 - 2024 DO - 10.35414/akufemubid.1500759 JF - Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi PB - Afyon Kocatepe University WT - DergiPark SN - 2149-3367 SP - 321 EP - 328 VL - 25 IS - 2 LA - en AB - In this paper, we present Legendre - collocation method, together with the Gauss–Legendre quadrature integration for solving fractional order delay-integro differential equations (FDIDE) with Caputo fractional derivative. The properties of shifted Legendre polynomials are used to solve the FDIDE to system of equations. The equation system obtained is solved by using Newton iteration method based on our present method with numerical examples is shown both applicability and efficiency of method. The results obtained by the collocation method are compared with exact solution and is shown to be compatible. The Maple and MATLAB programs are used for the calculations required in the study. KW - Fractional Delay Integro Differential Equation KW - Shifted Legendre Polynomials KW - Caputo Fractional Derivative KW - Gauss–Legendre Quadrature KW - Collocation Method N2 - Bu çalışmada, kesirli mertebeden gecikmeli integro diferansiyel denklemlerin nümerik çözümleri için Gauss-Legendre quadrature integrasyonu ile birlikte Caputo kesirli türevi ve Legendre kolokasyon yöntemi uygulanmıştır. Ötelenmiş Legendre polinomları yardımıyla denklem sistemi elde edilmiş ve kesirli mertebeden gecikmeli-integro diferansiyel denklemleri nümerik olarak çözülmüştür. Elde edilen denklem sistemi Newton iterasyon yöntemi kullanılarak çözülmüştür. Yöntemin uygulanabilirliği ve etkinliği sayısal örneklerle gösterilmiştir. Elde edilen sonuçlar tam çözümler ile karşılaştırılmış ve uyumlu olduğu gösterilmiştir. 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