  We consider the problem of waves propagating in a viscoelastic solid. For the
material properties of the solid we consider both classical and fractional
differentiation in time versions of the Zener, Maxwell, and Voigt models, where
the coupling of different models within the same solid are covered as well.
Stability of each model is investigated in the Laplace domain, and these are
then translated to time-domain estimates. With the use of semigroup theory,
some time-domain results are also given which avoid using the Laplace transform
and give sharper estimates. We take the time to develop and explain the theory
necessary to understand the relation between the equations we solve in the
Laplace domain and those in the time-domain which are written using the
language of causal tempered distributions. Finally we offer some numerical
experiments that highlight some of the differences between the models and how
different parameters effect the results.
