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2007, 2007(Special): 277-285. doi: 10.3934/proc.2007.2007.277

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, Spain

Received  September 2006 Revised  January 2007 Published  September 2007

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: sectorial kernels., convolution quadratures, asymptotic behaviour, Fractional equations.
Mathematics Subject Classification: Primary: 26A33, 45N05, 65J10; Secondary: 44A35, 65R2.
Citation: Eduardo Cuesta. Asymptotic behaviour of the solutions of fractional integro-differential equations and some time discretizations. Conference Publications, 2007, 2007 (Special) : 277-285. doi: 10.3934/proc.2007.2007.277
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