https://doi.org/10.1140/epjst/e2011-01388-0
Regular Article
Models based on Mittag-Leffler functions for anomalous relaxation in dielectrics
1 Department of Applied Mathematics, IMECC, University of Campinas, 13083-869 Campinas, SP, Brazil
2 Department of Physics, University of Bologna, via Irnerio 46, 40126 Bologna, Italy
a e-mail: capelas@ime.unicamp.br
b e-mail: francesco.mainardi@unibo.it
c e-mail: vaz@ime.unicamp.br
Received:
1
December
2010
Revised:
27
January
2011
Published online:
4
April
2011
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.
© EDP Sciences, Springer-Verlag, 2011