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A Lyapunov approach to the stability of fractional differential equations. (English) Zbl 1203.94059
Summary: Lyapunov stability of fractional differential equations is addressed in this paper. The key concept is the frequency distributed fractional integrator model, which is the basis for a global state space model of FDEs. Two approaches are presented: the direct one is intuitive but it leads to a large dimension parametric problem while the indirect one, which is based on the continuous frequency distribution, leads to a parsimonious solution. Two examples, with linear and nonlinear FDEs, exhibit the main features of this new methodology.
MSC:
94A12Signal theory (characterization, reconstruction, filtering, etc.)
34A08Fractional differential equations
93D05Lyapunov and other classical stabilities of control systems
References:
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