Lyapunov Fonksiyonları ile Fraksiyonel Diferansiyel Denklemlerin Kararlılığı

Abstract

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.

Keywords

• Asimptotik Kararlılık,Fraksiyonel Diferansiyel Denklemler,Lyapunov Fonksiyonları

On Stability of Fractional Differential Equations with Lyapunov Functions

Abstract

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.

Keywords

• Asymptotic Stability,Fractional Differential Equations,Lyapunov Functional

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