Models based on Mittag-Leffler functions for anomalous relaxation in dielectrics
By E. Capelas de Oliveira, Francesco Mainardi, Jayme Vaz Jr.. 2011
166 citations recorded by the source corpus.
Abstract.We revisit the Mittag-Leffler functions of a real variable t, with one, two and three order-parameters {α,β,γ}, as far as their Laplace transform pairs and complete monotonicity properties are concerned. These functions, subjected to the requirement to be completely monotone for t > 0, are shown to be suitable models for non–Debye relaxation phenomena in dielectrics including as particular cases the classical models referred to as Cole–Cole, Davidson–Cole and Havriliak–Negami. We show 3D plots of the relaxations functions and of the corresponding spectral distributions, keeping fixed one of the three order-parameters.
Subfields: Biomedical Engineering, Materials Chemistry, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/6225c1cb551f417888ff6ec42a40526e4f6c757f
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Biomedical Engineering
- Federico Polito
- Roberto Garrappa
- Virginia S. Kiryakova
- J. Machado
- Andrea Giusti
- Duarte Valério
- Roberto Garra
- Marina Popolizio
In Materials Chemistry
In Statistics and Probability
- Roberto Garrappa
- Federico Polito
- J. Machado
- Virginia S. Kiryakova
- Duarte Valério
- Francesco Mainardi
- Rudolf Gorenflo
- Om Prakash Agrawal
Citations in the corpus
- Some pioneers of the applications of fractional calculus (2013, methodology): “The Cole-Cole model [34] was one of the first applications of FC and plays nowadays an important role in many different scientific areas.”
- A practical guide to Prabhakar fractional calculus (2020, background): “First, the conditions for the complete monotonicity of the Prabhakar function have been extensively analyzed throughout the last decade in [12, 97, 149] by several authors.”