{
  "id": "2001.06856",
  "version": "v1",
  "published": "2020-01-19T16:14:30.000Z",
  "updated": "2020-01-19T16:14:30.000Z",
  "title": "Anomalous relaxation in dielectrics with Hilfer fractional derivative",
  "authors": [
    "A. R. Gomez Plata",
    "Ester C. A. F. Rosa",
    "R. G Rodriguez-Giraldo",
    "E. Capelas de Oliveira"
  ],
  "comment": "20 pages",
  "categories": [
    "cond-mat.stat-mech",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We introduce a new relaxation function depending on an arbitrary parameter as solution of a kinetic equation in the same way as the relaxation function introduced empirically by Debye, Cole-Cole, Davidson-Cole and Havriliak-Negami, anomalous relaxation in dielectrics, which are recovered as particular cases. We propose a differential equation introducing a fractional operator written in terms of the Hilfer fractional derivative of order {\\xi}, with 0<{\\xi}<1 and type {\\eta}, with 0<{\\eta}<1. To discuss the solution of the fractional differential equation, the methodology of Laplace transform is required. As a by product we mention particular cases where the solution is completely monotone. Finally, the empirical models are recovered as particular cases.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-19T16:14:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hilfer fractional derivative",
      "anomalous relaxation",
      "dielectrics",
      "relaxation function",
      "fractional differential equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}