{
  "id": "1106.1761",
  "version": "v2",
  "published": "2011-06-09T09:50:49.000Z",
  "updated": "2014-02-13T08:45:34.000Z",
  "title": "Models based on Mittag-Leffler functions for anomalous relaxation in dielectrics",
  "authors": [
    "Edmundo Capelas de Oliveira",
    "Francesco Mainardi",
    "Jayme Vaz Jr"
  ],
  "comment": "22 pages, 6 figures, Second Revised Version",
  "journal": "The European Physical Journal, Special Topics, Vol. 193 (2011), pp. 161-171",
  "categories": [
    "cond-mat.stat-mech",
    "math-ph",
    "math.MP"
  ],
  "abstract": "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 monotonicty 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 response functions and of the corresponding spectral distributions, keeping fixed one of the three order-parameters.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-02-13T08:45:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26A33",
      "33E12",
      "44A10"
    ],
    "keywords": [
      "mittag-leffler functions",
      "anomalous relaxation",
      "dielectrics",
      "laplace transform pairs",
      "complete monotonicty properties"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1140/epjst/e2011-01388-0",
      "journal": "European Physical Journal Special Topics",
      "year": 2011,
      "month": "Mar",
      "volume": 193,
      "pages": 161
    },
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011EPJST.193..161C"
    }
  }
}