Asymptotic behaviour of the solutions of fractional integro-differential equations and some time discretizations

Pages: 277 - 285, Issue Special, September 2007

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Eduardo Cuesta - Department of Applied Mathematics E.U.P. de Valladolid, C/ Francisco Mendizabal, 1, Valladolid 47014, Spain (email)

Abstract: We study he asymptotic behaviour as $t \rightarrow + \infty$ of the solutions of an abstract fractional equation $u = u_0 + \partial^( - \alpha) Au + g$, 1 < $\alpha$ < 2, where $A$ is a linear operator of sectorial type. We also show that a discretization in time of this equation based on backward Euler convolution quadrature inherits this behaviour.

Keywords:  Fractional equations, convolution quadratures, asymptotic behaviour, sectorial kernels.
Mathematics Subject Classification:  Primary: 26A33, 45N05, 65J10; Secondary: 44A35, 65R20.

Received: September 2006;      Revised: January 2007;      Published: September 2007.