  The characteristic (Laplace or L\'evy) exponents uniquely characterize
infinitely divisible probability distributions. Although of purely mathematical
origin they appear to be uniquely associated with the memory functions present
in evolution equations which govern the course of such physical phenomena like
non-Debye relaxations or anomalous diffusion. Commonly accepted procedure to
mimic memory effects is to make basic equations time smeared, i.e., nonlocal in
time. This is modeled either through the convolution of memory functions with
those describing relaxation/diffusion or, alternatively, through the time
smearing of time derivatives. Intuitive expectations say that such introduced
time smearings should be physically equivalent. This leads to the conclusion
that both kinds of so far introduced memory functions form a "twin" structure
familiar to mathematicians for a long time and known as the Sonine pair. As an
illustration of the proposed scheme we consider the excess wings model of
non-Debye relaxations, determine its evolution equations and discuss properties
of the solutions.
