Hanta-virüs Modelinden Elde Edilen Lojistik Diferansiyel Denklem

Year 2016, Volume: 11 Issue: 1, 82 - 91, 24.05.2016

Zarife Gökçen Karadem Mevlüde Yakıt Ongun

Abstract

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.

Keywords

Kesirli Diferansiyel Denklem, Hanta-virüs, Lojistik Diferansiyel Denklem

References

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