{
  "id": "1510.00315",
  "version": "v1",
  "published": "2015-10-01T16:57:59.000Z",
  "updated": "2015-10-01T16:57:59.000Z",
  "title": "Fractional diffusion equation with distributed-order material derivative. Stochastic foundations",
  "authors": [
    "Marcin Magdziarz",
    "Marek Teuerle"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper we present stochastic foundations of fractional dynamics driven by fractional material derivative of distributed order-type. Before stating our main result we present the stochastic scenario which underlies the dynamics given by fractional material derivative. Then we introduce a Levy walk process of distributed-order type to establish our main result, which is the scaling limit of the considered process. It appears that the probability density function of the scaling limit process fulfills, in a weak sense, the fractional diffusion equation with material derivative of distributed-order type.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-01T16:57:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34A08",
      "26A33",
      "60F17",
      "60G50",
      "60G51",
      "60B05",
      "60J75"
    ],
    "keywords": [
      "fractional diffusion equation",
      "stochastic foundations",
      "distributed-order material derivative",
      "fractional material derivative",
      "main result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}