Journal
EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS
Volume 193, Issue 1, Pages 161-171Publisher
SPRINGER HEIDELBERG
DOI: 10.1140/epjst/e2011-01388-0
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- FAEPEX [184/10]
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We revisit the Mittag-Leffler functions of a real variable t, with one, two and three order-parameters {alpha, beta, gamma}, 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.
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