The non-Debye, i.e., non-exponential, behavior characterizes a large plethora of dielectric relaxation phenomena. Attempts to find their theoretical explanation are dominated either by considerations rooted in the stochastic processes methodology or by the so-called fractional dynamics based on equations involving fractional derivatives which mimic the non-local time evolution and as such may be interpreted as describing memory effects. Using the recent results coming from the stochastic approach we link memory functions with the Laplace (characteristic) exponents of infinitely divisible probability distributions and show how to relate the latter with experimentally measurable spectral functions characterizing relaxation in the frequency domain. This enables us to incorporate phenomenological knowledge into the evolution laws. To illustrate our approach we consider the standard Havriliak-Negami and Jurlewicz-Weron-Stanislavsky models for which we derive well-defined evolution equations. Merging stochastic and fractional dynamics approaches sheds also new light on the analysis of relaxation phenomena which description needs going beyond using the single evolution pattern. We determine sufficient conditions under which such description is consistent with general requirements of our approach.

非德拜（即非指数）行为表征了大量介电弛豫现象。试图找到其理论解释的原因要么是基于随机过程方法的考虑，要么是所谓的分数动力学。基于涉及模拟非局部时间演变的分数导数的方程，因此可以解释为描述记忆效应。使用来自随机方法的最新结果，我们将记忆函数与无限可分概率分布的拉普拉斯（特征）指数联系起来，并展示了如何将后者与表征频域弛豫的实验可测量频谱函数联系起来。这使我们能够将现象学知识纳入进化定律。为了说明我们的方法，我们考虑标准的Havriliak-Negami和Jurlewicz-Weron-Stanislavsky模型，从中得出定义明确的演化方程。随机和分数动力学方法的融合也为松弛现象的分析提供了新的思路，松弛现象的分析需要超越单一的演化模式。我们确定了充分的条件，在这种条件下，这种描述与我们的方法的一般要求相一致。