{
  "id": "2001.10846",
  "version": "v1",
  "published": "2020-01-29T14:02:11.000Z",
  "updated": "2020-01-29T14:02:11.000Z",
  "title": "About Convergence and Order of Convergence of some Fractional Derivatives",
  "authors": [
    "Sabrina Roscani",
    "Lucas Venturato"
  ],
  "comment": "16 oages, 4 figures",
  "categories": [
    "math.AP",
    "cs.NA",
    "math.CA",
    "math.NA"
  ],
  "abstract": "In this paper we establish some convergence results for Riemann-Liouville, Caputo, and Caputo-Fabrizio fractional operators when the order of differentiation approaches one. We consider some errors given by $\\left|\\left| D^{1-\\al}f -f'\\right|\\right|_p$ for p=1 and $p=\\infty$ and we prove that for both Caputo and Caputo Fabrizio operators the order of convergence is a positive real r, 0<r<1. Finally, we compare the speed of convergence between Caputo and Caputo-Fabrizio operators obtaining that they a related by the Digamma function.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-29T14:02:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26A33",
      "41A25",
      "47G20"
    ],
    "keywords": [
      "fractional derivatives",
      "caputo-fabrizio fractional operators",
      "caputo fabrizio operators",
      "digamma function",
      "differentiation approaches"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}