Hanta-virüs Modelinden Elde Edilen Lojistik Diferansiyel Denklem

Authors : Zarife Gökçen KARADEM, Mevlüde YAKIT ONGUN

Pages : 82-91

View : 41 | Download : 16

Publication Date : 2016-05-24

Article Type : Research Paper

Abstract :Kesirli mertebeden Hanta-virüs modeli olarak alınan lineer olmayan diferansiyel denklem sistemi 〖insert ignore into journalissuearticles values(_c^);D〗_insert ignore into journalissuearticles values(0,t);^α Xinsert ignore into journalissuearticles values(t);=insert ignore into journalissuearticles values(b-c);Xinsert ignore into journalissuearticles values(t);+bYinsert ignore into journalissuearticles values(t);-insert ignore into journalissuearticles values(X^2 insert ignore into journalissuearticles values(t););/K-insert ignore into journalissuearticles values(insert ignore into journalissuearticles values(1+aK);/K);Xinsert ignore into journalissuearticles values(t);Yinsert ignore into journalissuearticles values(t); 〖insert ignore into journalissuearticles values(_c^);D〗_insert ignore into journalissuearticles values(0,t);^α Yinsert ignore into journalissuearticles values(t);=-cYinsert ignore into journalissuearticles values(t);-insert ignore into journalissuearticles values(Y^2 insert ignore into journalissuearticles values(t););/K-insert ignore into journalissuearticles values(insert ignore into journalissuearticles values(1-aK);/K);Xinsert ignore into journalissuearticles values(t);Yinsert ignore into journalissuearticles values(t); insert ignore into journalissuearticles values(1); şeklinde tanımlanmıştır. Burada 〖insert ignore into journalissuearticles values(_c^);D〗_insert ignore into journalissuearticles values(0,t);^α kesirli türev insert ignore into journalissuearticles values(Caputo); operatörünü göstermektedir. insert ignore into journalissuearticles values(1); sistemini ayrıklaştırmak için Grünwald-Letnikov türev operatörü ve Standart Olmayan Sonlu Farklar insert ignore into journalissuearticles values(SOSF); Yöntemi uygulanacaktır. insert ignore into journalissuearticles values(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 〖insert ignore into journalissuearticles values(_c^);D〗_insert ignore into journalissuearticles values(0,t);^α Xinsert ignore into journalissuearticles values(t);=insert ignore into journalissuearticles values(b-c);Xinsert ignore into journalissuearticles values(t);+bYinsert ignore into journalissuearticles values(t);-insert ignore into journalissuearticles values(X^2 insert ignore into journalissuearticles values(t););/K-insert ignore into journalissuearticles values(insert ignore into journalissuearticles values(1+aK);/K);Xinsert ignore into journalissuearticles values(t);Yinsert ignore into journalissuearticles values(t); 〖insert ignore into journalissuearticles values(_c^);D〗_insert ignore into journalissuearticles values(0,t);^α Yinsert ignore into journalissuearticles values(t);=-cYinsert ignore into journalissuearticles values(t);-insert ignore into journalissuearticles values(Y^2 insert ignore into journalissuearticles values(t););/K-insert ignore into journalissuearticles values(insert ignore into journalissuearticles values(1-aK);/K);Xinsert ignore into journalissuearticles values(t);Yinsert ignore into journalissuearticles values(t); insert ignore into journalissuearticles values(1); Here, 〖insert ignore into journalissuearticles values(_c^);D〗_insert ignore into journalissuearticles values(0,t);^α denotes the fractional derivative insert ignore into journalissuearticles values(Caputo); operator. The Grünwald-Letnikov operator and Nonstandart Finite Diference insert ignore into journalissuearticles values(SOSF); schemes will be applied to discretize the fractional-order nonlinear system insert ignore into journalissuearticles values(1);. Fractional order logistic equation optioned with some adjustments in insert ignore into journalissuearticles values(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

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