Lyapunov functions and convergence to steady state for differential equations of fractional order期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Lyapunov functions and convergence to steady state for differential equations of fractional order

Authors:	Vicente Vergara Rico Zacher

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

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 $\mathcal E$ occurring in the equation satisfies the Łojasiewicz inequality.

Keywords:	Integro-differential equations Fractional derivative Gradient system Lyapunov function Convergence to steady state Ł ojasiewicz inequality
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