Lyapunov functions and convergence to steady state for differential equations of fractional order |
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Authors: | Vicente Vergara Rico Zacher |
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Institution: | 1. Departamento de Matemática y C.C., Facultad de Ciencias, University of Santiago de Chile, Casilla 307, Correo 2, Santiago, Chile 2. Institut für Mathematik, Martin-Luther-Universit?t Halle-Wittenberg, Theodor-Lieser-Strasse 5, 06120, Halle, Germany
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Abstract: | We study the asymptotic behaviour, as t → ∞, of bounded solutions to certain integro-differential equations in finite dimensions which include differential equations
of fractional order between 0 and 2. We derive appropriate Lyapunov functions for these equations and prove that any global
bounded solution converges to a steady state of a related equation, if the nonlinear potential occurring in the equation satisfies the Łojasiewicz inequality.
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Keywords: | Integro-differential equations Fractional derivative Gradient system Lyapunov function Convergence to steady state Ł ojasiewicz inequality |
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