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

Eduardo Cuesta

doi:10.3934/proc.2007.2007.277

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2007, Volume 2007: 277-285. Doi: 10.3934/proc.2007.2007.277 open access

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

Eduardo Cuesta^1,

1.
Department of Applied Mathematics E.U.P. de Valladolid, C/ Francisco Mendizabal, 1, Valladolid 47014

Received: September 2006

Revised: January 2007

Published: August 2007

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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.

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Mathematics Subject Classification: Primary: 26A33, 45N05, 65J10; Secondary: 44A35, 65R20.

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