The characteristic (Laplace or Lévy) 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.

特征（拉普拉斯或列维）指数唯一地表征了无限可分的概率分布。尽管纯粹是数学起源，但它们似乎与进化方程中存在的记忆函数唯一相关，这些函数控制着非德拜松弛或异常扩散等物理现象的进程。普遍接受的模拟记忆效应的程序是使基本方程时间涂抹，即时间上的非局部性。这是通过记忆函数与描述松弛/扩散的函数的卷积或通过时间导数的时间涂抹来建模的。直观的预期表明，这种引入的时间拖尾应该在物理上是等效的。由此得出的结论是，迄今为止引入的两种记忆功能形成了数学家长期以来熟悉的“双胞胎”结构，并被称为 Sonine 对。作为所提出方案的说明，我们考虑非德拜松弛的多余翼模型，确定其演化方程并讨论解的性质。