  We present a new approach based on linear integro-differential operators with
logarithmic kernel related to the Hadamard fractional calculus in order to
generalize, by a parameter $\nu \in (0,1]$, the logarithmic creep law known in
rheology as Lomnitz law (obtained for $\nu=1$). We derive the constitutive
stress-strain relation of this generalized model in a form that couples memory
effects and time-varying viscosity. Then, based on the hereditary theory of
linear viscoelasticity, we also derive the corresponding relaxation function by
solving numerically a Volterra integral equation of the second kind. So doing
we provide a full characterization of the new model both in creep and in
relaxation representation, where the slow varying functions of logarithmic type
play a fundamental role as required in processes of ultra slow kinetics.
