  As well known, the generalized Langevin equation with a memory kernel
decreasing at large times as an inverse power law of time describes the motion
of an anomalously diffusing particle. Here, we focus attention on some new
aspects of the dynamics, successively considering the memory kernel, the
particle's mean velocity, and the scattering function. All these quantities are
studied from a unique angle, namely, the discussion of the possible existence
of a distribution of relaxation times characterizing their time decay. Although
a very popular concept, a relaxation time distribution cannot be associated
with any time-decreasing quantity (from a mathematical point of view, the decay
has to be described by a completely monotonic function). Technically, we use a
memory kernel decaying as a Mittag-Leffler function (the Mittag-Leffler
functions interpolate between stretched or compressed exponential behaviour at
short times and inverse power law behaviour at large times). We show that, in
the case of a subdiffusive motion, relaxation time distributions can be defined
for the memory kernel and for the scattering function, but not for the
particle's mean velocity. The situation is opposite in the superdiffusive case.
