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 |