Zarife Gökçen KARADEM, Mevlüde YAKIT ONGUN

Hanta-virüs Modelinden Elde Edilen Lojistik Diferansiyel Denklem

Kesirli mertebeden Hanta-virüs modeli olarak alınan lineer olmayan diferansiyel denklem sistemi 〖(_c^)D〗_(0,t)^α X(t)=(b-c)X(t)+bY(t)-(X^2 (t))/K-((1+aK)/K)X(t)Y(t) 〖(_c^)D〗_(0,t)^α Y(t)=-cY(t)-(Y^2 (t))/K-((1-aK)/K)X(t)Y(t) (1) şeklinde tanımlanmıştır. Burada 〖(_c^)D〗_(0,t)^α kesirli türev (Caputo) operatörünü göstermektedir. (1) sistemini ayrıklaştırmak için Grünwald-Letnikov türev operatörü ve Standart Olmayan Sonlu Farklar (SOSF) Yöntemi uygulanacaktır. (1) sistemindeki bazı düzenlemeler ile kesirli mertebeden Lojistik denklem elde edilip, bulgular bazı grafikler ve tablolar yardımı ile desteklenecektir. Anahtar kelimeler: Kesirli Diferansiyel Denklem, Hanta-virüs, Lojistik Diferansiyel Denklem. Logistic Differential Equations Obtained from Hanta-virus Model Abstract: Fractional-order Hanta-virüs Model as received nonlinear differential equation system is 〖(_c^)D〗_(0,t)^α X(t)=(b-c)X(t)+bY(t)-(X^2 (t))/K-((1+aK)/K)X(t)Y(t) 〖(_c^)D〗_(0,t)^α Y(t)=-cY(t)-(Y^2 (t))/K-((1-aK)/K)X(t)Y(t) (1) Here, 〖(_c^)D〗_(0,t)^α denotes the fractional derivative (Caputo) operator. The Grünwald-Letnikov operator and Nonstandart Finite Diference (SOSF) schemes will be applied to discretize the fractional-order nonlinear system (1). Fractional order logistic equation optioned with some adjustments in (1) system. The findings will be supported with the help of some of the graphs and tables. Key words: Fractional diferantial equation, Hanta-virus, Logistic Differential Equation.

Anahtar Kelimeler:

Kesirli Diferansiyel Denklem, Hanta-virüs, Lojistik Diferansiyel Denklem

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