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

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


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