  We use the two-time scale subordination in order to describe dynamical
processes in continuous media with a long-term memory. Our consideration
touches two physical examples in detail. First we study a temporal evolution of
the species concentration for the trapping reaction in which a diffusing
reactant is surrounded by a sea of randomly moving traps. The analysis is based
on the random-variable formalism of anomalous diffusive processes. We find that
the empirical trapping-reaction law, according to which the reactant
concentration decreases in time as a product of an exponential and a stretched
exponential function, can be explained by the two-time scale subordination of
random processes. Another example is connected with a state equation for
continuous media with memory. If the pressure and the density of a medium are
subordinated in two different random processes, then the ordinary state
equation becomes fractional with two time scales. This allows one to arrive at
the state equation of Bagley-Torvik type.
