Kesirli Mertebeden Gecikmeli-İntegro Diferansiyel Denklemler için Etkili Yöntemler

Yıl 2025, Cilt: 25 Sayı: 2, 321 - 328

Eda Akarsu , Mustafa Gülsu

Öz

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. Tüm hesaplamalar için Maple ve MATLAB programları kullanılmıştır.

Anahtar Kelimeler

Kesirli Gecikmeli İntegro Dİferansiyel Denklem, Ötelenmiş Legendre Polinomları, Caputo Kesirli Türevi, Gauss-Legendre Quadrature, Kolokasyon Metodu

Etik Beyan

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Destekleyen Kurum

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Proje Numarası

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Teşekkür

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Efficient Computational Techniques for Fractional Order Delay-Integro Differential Equations

Öz

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.

Anahtar Kelimeler

Fractional Delay Integro Differential Equation, Shifted Legendre Polynomials, Caputo Fractional Derivative, Gauss–Legendre Quadrature, Collocation Method

Proje Numarası

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Kaynakça

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