{
  "id": "math/0607140",
  "version": "v1",
  "published": "2006-07-05T19:24:17.000Z",
  "updated": "2006-07-05T19:24:17.000Z",
  "title": "Numerical solutions to boundary value problem for anomalous diffusion equation with Riesz-Feller fractional operator",
  "authors": [
    "Mariusz Ciesielski",
    "Jacek Leszczynski"
  ],
  "comment": "11 pages, 4 figures",
  "journal": "Journal of Theoretical and Applied Mechanics 44, 2, pp. 393-403, Warsaw 2006",
  "categories": [
    "math.NA",
    "math.AP"
  ],
  "abstract": "In this paper, we present a numerical solution to an ordinary differential equation of a fractional order in one-dimensional space. The solution to this equation can describe a steady state of the process of anomalous diffusion. The process arises from interactions within complex and non-homogeneous background. We present a numerical method which is based on the finite differences method. We consider a boundary value problem (Dirichlet conditions) for an equation with the Riesz-Feller fractional derivative. In the final part of this paper, same simulation results are shown. We present an example of non-linear temperature profiles in nanotubes which can be approximated by a solution to the fractional differential equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-07-05T19:24:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "boundary value problem",
      "riesz-feller fractional operator",
      "anomalous diffusion equation",
      "numerical solution",
      "fractional differential equation"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}