This article establishes a link between molecular theories that predict the macroscopic behavior of certain viscoelastic media and an empirically developed fractional calculus approach to viscoelasticity. The molecular theory addresses the viscoelastic properties of polymer solids with no crosslinking. It is shown that the results of these molecular theories are equivalent to constitutive relationships written in terms of the fractional calculus. Such relationships, developed previously from an empirical base, have been shown to be useful tools for engineering analyses. The establishment of a theoretical basis for these new constitutive relationships enhances their value, as they may now be used with increased confidence.