{
  "id": "2009.12977",
  "version": "v1",
  "published": "2020-09-27T23:01:23.000Z",
  "updated": "2020-09-27T23:01:23.000Z",
  "title": "The similarity method and explicit solutions for the fractional space one-phase Stefan problems",
  "authors": [
    "S. D. Roscani",
    "D. A. Tarzia",
    "L. Venturato"
  ],
  "comment": "20 pages, 1 figure",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we obtain self-similarity solutions for a one-phase one-dimensional fractional space one-phase Stefan problem in terms of the three parametric Mittag-Leffer function $E_{\\alpha,m;l}(z)$. We consider Dirichlet and Newmann conditions at the fixed face, involving Caputo fractional space derivatives of order $0 < \\alpha < 1$. We recover the solution for the classical one-phase Stefan problem when the order of the Caputo derivatives approaches one.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-27T23:01:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26A33",
      "35C06",
      "35R11",
      "35R35",
      "80A22"
    ],
    "keywords": [
      "fractional space one-phase stefan problem",
      "explicit solutions",
      "similarity method",
      "one-phase one-dimensional fractional space one-phase",
      "one-dimensional fractional space one-phase stefan"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}