  Stochastic processes driven by stationary fractional Gaussian noise, that is,
fractional Brownian motion and fractional Langevin equation motion, are usually
considered to be ergodic in the sense that, after an algebraic relaxation, time
and ensemble averages of physical observables coincide. Recently it was
demonstrated that fractional Brownian motion and fractional Langevin equation
motion under external confinement are transiently non-ergodic---time and
ensemble averages behave differently---from the moment when the particle starts
to sense the confinement. Here we show that these processes also exhibit
transient ageing, that is, physical observables such as the time averaged mean
squared displacement depend on the time lag between the initiation of the
system at time $t=0$ and the start of the measurement at the ageing time $t_a$.
In particular, it turns out that for fractional Langevin equation motion the
ageing dependence on $t_a$ is different between the cases of free and confined
motion. We obtain explicit analytical expressions for the aged moments of the
particle position as well as the time averaged mean squared displacement and
present a numerical analysis of this transient ageing phenomenon.
