  The one-dimensional fractional derivative Maxwell model (e.g. Palade et al.
Rheol. Acta 35, 265, 1996), of importance in modeling the linear viscoelastic
response in the glass transition region, has been generalized in Palade et al.
Int. J. Non-Linear Mech. 37, 315, 1999, to objective three-dimensional
constitutive equations (CEs) for both fluids and solids. Regarding the rest
state stability of the fluid CE, in Heibig and Palade J. Math. Phys. 49,
043101, 2008, we gave a proof for the existence of weak solutions to the
corresponding boundary value problem. The aim of this work is to achieve the
study of the existence and uniqueness of the aforementioned solutions and to
present smoothness results.
