In the literature, fractional models are commonly approximated by transfer functions with a geometric distribution of poles and zeros, or equivalently, using electrical Foster or Cauer type networks with components whose values also meet geometric distributions. This paper first shows that this geometric distribution is only a particular distribution case and that many other distributions (an infinity) are in fact possible. From the networks obtained, a class of partial differential equations (heat equation with a spatially variable coefficient) is then deduced. This class of equations is thus another tool for power law type long memory behaviour modelling, that solves the drawback inherent in fractional heat equations that was proposed to model anomalous diffusion phenomena.

在文献中，分数模型通常通过极点和零点的几何分布的传递函数来近似估计，或者等效地，使用具有其值也符合几何分布的电子Foster或Cauer型网络。本文首先表明，这种几何分布只是一个特殊的分布情况，实际上许多其他分布（无穷大）也是可能的。然后从获得的网络中推导一类偏微分方程（具有空间可变系数的热方程）。因此，这类方程是幂律类型长记忆行为建模的另一种工具，解决了分数热方程中固有的缺陷，这种缺陷被提出来模拟异常扩散现象。