Non-Debye relaxations: The characteristic exponent in the excess wings model

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