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.