Preprint series: 07-14 , Reports on Analysis
Abstract: We study the asymptotic behaviour, as $t\to\infty$, 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 ${\cal E}$ occurring in the equation satisfies the \L ojasiewicz inequality.
Keywords: integro-differential equations, fractional derivative, gradient system, Lyapunov function, convergence to steady state, Lojasiewicz inequality
Upload: 2007-07-25