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.
Keywords: Cauer networks; Foster networks; Fractional models; Heat equation; Poles and zeros geometric distributions; Power law type long memory behaviours.
© 2020 The Authors. Published by Elsevier B.V. on behalf of Cairo University.