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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.
94A12Signal theory (characterization, reconstruction, filtering, etc.)
34A08Fractional differential equations
93D05Lyapunov and other classical stabilities of control systems
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