  Fractional Brownian motion and the fractional Langevin equation are models of
anomalous diffusion processes characterized by long-range power-law
correlations in time. We employ large-scale computer simulations to study these
models in two geometries, (i) the spreading of particles on a semi-infinite
domain with an absorbing wall at one end and (ii) the stationary state on a
finite interval with absorbing boundaries at both ends and a source in the
center. We demonstrate that the probability density and other properties of the
fractional Langevin equation can be mapped onto the corresponding quantities of
fractional Brownian motion driven by the same noise if the anomalous diffusion
exponent $\alpha$ is replaced by $2-\alpha$. In contrast, the properties of
fractional Brownian motion and the fractional Langevin equation with reflecting
boundaries were recently shown to differ from each other qualitatively.
Specifically, we find that the probability density close to an absorbing wall
behaves as $P(x) \sim x^\kappa$ with the distance $x$ from the wall in the
long-time limit. In the case of fractional Brownian motion, $\kappa$ varies
with the anomalous diffusion exponent $\alpha$ as $\kappa=2/\alpha -1$, as was
conjectured previously. We also compare our simulation results to a
perturbative analytical approach to fractional Brownian motion.
