  Mesoscopic non-equilibrium thermodynamics is used to formulate a model
describing non-homogeneous and non-Debye dielectric relaxation. The model is
presented in terms of a Fokker-Planck equation for the probability distribution
of non-interacting polar molecules in contact with a heat bath and in the
presence of an external time-dependent electric field. Memory effects are
introduced in the Fokker-Planck description through integral relations
containing memory kernels, which in turn are used to establish a connection
with fractional Fokker-Planck descriptions. The model is developed in terms of
the evolution equations for the first two moments of the distribution function.
These equations are solved by following a perturbative method from which the
expressions for the complex susceptibilities are obtained as a functions of the
frequency and the wave number. Different memory kernels are considered and used
to compare with experiments of dielectric relaxation in glassy systems. For the
case of Cole-Cole relaxation, we infer the distribution of relaxation times and
its relation with an effective distribution of dipolar moments that can be
attributed to different segmental motions of the polymer chains in a melt.
