{
  "id": "cond-mat/0701132",
  "version": "v2",
  "published": "2007-01-07T15:10:01.000Z",
  "updated": "2007-09-30T10:34:12.000Z",
  "title": "Time-fractional diffusion of distributed order",
  "authors": [
    "Francesco Mainardi",
    "Antonio Mura",
    "Gianni Pagnini",
    "Rudolf Gorenflo"
  ],
  "comment": "30 pages, 4 figures. International Workshop on Fractional Differentiation and its Applications (FDA06), 19-21 July 2006, Porto, Portugal. Journal of Vibration and Control, in press (2007)",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.dis-nn",
    "math-ph",
    "math.MP"
  ],
  "abstract": "The partial differential equation of Gaussian diffusion is generalized by using the time-fractional derivative of distributed order between 0 and 1, in both the Riemann-Liouville (R-L) and the Caputo (C) sense. For a general distribution of time orders we provide the fundamental solution, that is still a probability density, in terms of an integral of Laplace type. The kernel depends on the type of the assumed fractional derivative except for the single order case where the two approaches turn to be equivalent. We consider with some detail two cases of order distribution: the double-order and the uniformly distributed order. For these cases we exhibit plots of the corresponding fundamental solutions and their variance, pointing out the remarkable difference between the two approaches for small and large times.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-09-30T10:34:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "distributed order",
      "time-fractional diffusion",
      "partial differential equation",
      "single order case",
      "approaches turn"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007cond.mat..1132M"
    }
  }
}