A model of relaxation in supercooled and entangled polymer liquids is devel
oped starting from an integral equation describing relaxation in liquids ne
ar thermal equilibrium and probabilistic modelling of the dynamic heterogen
eity presumed to occur in these complex fluids. The treatment of stress rel
axation considers two types of dynamic heterogeneity-temporal heterogeneity
reflecting the intermittency of particle motion in cooled liquids and spat
ial heterogeneity or particle clustering governed by Boltzmann's law. Exact
solution of the model relaxation integral equation by fractional calculus
methods leads to a two parameter family of relaxation functions for which t
he memory indices (beta, phi) provide measures of the influence of the temp
oral and spatial heterogeneity on the relaxation process. The exponent beta
is related to the geometrical form of the spatial heterogeneity. Relaxatio
n function classes are identified according to the asymptotics of the psi(t
; beta, phi) functions at long and short times and their integrability prop
erties. The integral equation model for relaxation provides a framework for
understanding the existence of 'universality' in condensed matter relaxati
on under restricted circumstances.