Lyapunov Fonksiyonları ile Fraksiyonel Diferansiyel Denklemlerin Kararlılığı

Yıl 2019, Cilt: 7 Sayı: 1, 635 - 638, 30.06.2019

Erdal Korkmaz , Abdulhamit Özdemir

https://doi.org/10.18586/msufbd.559400

Cited By: 3

Öz

Bu çalışmada, fraksiyonel ve tamsayı mertebe içeren lineer
olmayan otonom diferansiyel denklem sistemlerinin asimptotik kararlılığı
araştırıldı. Lineer olmayan otonom fraksiyonel sistemlerin asimptotik
kararlılığını göstermek için bazı yeterli şartlar elde edilerek Lyapunov’un ikinci
metodu kullanıldı. Ayrıca elde edilen sonuçları pekiştirmek için iki örnek
verildi.

Anahtar Kelimeler

Asimptotik Kararlılık, Fraksiyonel Diferansiyel Denklemler, Lyapunov Fonksiyonları

On Stability of Fractional Differential Equations with Lyapunov Functions

Öz

We
discuss the asymptotic stability of autonomous nonlinear fractional order systems,
in which the state equations contain integer derivative and fractional order.
We use the Lyapunov's second method to derive some sufficient conditions to
ensure asymptotic stability of nonlinear fractional order differential
equations. We also give two examples in order to consolidate the obtained
results.

Anahtar Kelimeler

Asymptotic Stability, Fractional Differential Equations, Lyapunov Functional

Kaynakça

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