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Asymptotic behaviour of the solutions of fractional integro-differential equations and some time discretizations. (English) Zbl 1163.45306

Summary: We study the asymptotic behaviour as \(t\to+\infty\) 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.

MSC:

45M05 Asymptotics of solutions to integral equations
26A33 Fractional derivatives and integrals
45N05 Abstract integral equations, integral equations in abstract spaces
65J10 Numerical solutions to equations with linear operators
44A35 Convolution as an integral transform
65R20 Numerical methods for integral equations
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