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Generalized Mittag-Leffler stability of multi-variables fractional order nonlinear systems. (English) Zbl 1360.93513

Summary: In this paper, the stability of multi-variable fractional order nonlinear dynamic system is investigated. We propose the definition of generalized Mittag-Leffler stability with multi-variable and introduce the fractional Lyapunov direct method with multi-variable. Meanwhile, a novel approach is suggested to study generalized Mittag-Leffler stability in multi-variable fractional order nonlinear dynamic systems. An interesting multi-variable fractional order Lotka-Volterra predator-prey model is used to illustrate the proposed method and its effectiveness.

MSC:

93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
34A08 Fractional ordinary differential equations
93C10 Nonlinear systems in control theory
91A24 Positional games (pursuit and evasion, etc.)
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