{
  "id": "1308.0451",
  "version": "v1",
  "published": "2013-08-02T10:07:43.000Z",
  "updated": "2013-08-02T10:07:43.000Z",
  "title": "Uniform approximation of fractional derivatives and integrals with application to fractional differential equations",
  "authors": [
    "Hassan Khosravian-Arab",
    "Delfim F. M. Torres"
  ],
  "comment": "This is a preprint of a paper whose final and definite form will appear in Nonlinear Studies, ISSN: 1359-8678 (print) 2153-4373 (online). Paper submitted 12-March-2013; accepted for publication 29-July-2013",
  "journal": "Nonlinear Stud. 20 (2013), no. 4, 533--548",
  "categories": [
    "math.CA",
    "math.NA"
  ],
  "abstract": "It is well known that for every $f\\in C^m$ there exists a polynomial $p_n$ such that $p^{(k)}_n\\rightarrow f^{(k)}$, $k=0,\\ldots,m$. Here we prove such a result for fractional (non-integer) derivatives. Moreover, a numerical method is proposed for fractional differential equations. The convergence rate and stability of the proposed method are obtained. Illustrative examples are discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-08-02T10:07:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26A33",
      "34A08",
      "41A10",
      "41A25"
    ],
    "keywords": [
      "fractional differential equations",
      "fractional derivatives",
      "uniform approximation",
      "application",
      "convergence rate"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1308.0451K"
    }
  }
}