  We present and review several models of fractional viscous stresses from the
literature, which generalise classical viscosity theories to fractional orders
by replacing total strain derivatives in time with fractional time derivatives.
We also briefly introduce Prony-type approximations of these theories. Here we
investigate the issues of material frame-indifference and thermodynamic
consistency for these models and find that on these bases, some are physically
unacceptable. Next we study elementary shearing and tensile motions, observing
that some models are more convenient to use than others for the analysis of
creep and relaxation. Finally, we compute the incremental stresses due to
small-amplitude wave propagation in a deformed material, with a view to
establish acousto-elastic formulas for prospective experimental calibrations.
