{
  "id": "1208.2588",
  "version": "v1",
  "published": "2012-08-13T13:49:11.000Z",
  "updated": "2012-08-13T13:49:11.000Z",
  "title": "Numerical Approximations of Fractional Derivatives with Applications",
  "authors": [
    "Shakoor Pooseh",
    "Ricardo Almeida",
    "Delfim F. M. Torres"
  ],
  "comment": "This is a preprint of a paper whose final and definite form will be published in: Asian Journal of Control. Submitted 13-Oct-2011; revised 11-Apr-2012; accepted 10-Aug-2012",
  "journal": "Asian Journal of Control 15 (2013), no. 3, 698--712",
  "doi": "10.1002/asjc.617",
  "categories": [
    "math.OC",
    "math.NA"
  ],
  "abstract": "Two approximations, derived from continuous expansions of Riemann-Liouville fractional derivatives into series involving integer order derivatives, are studied. Using those series, one can formally transform any problem that contains fractional derivatives into a classical problem in which only derivatives of integer order are present. Corresponding approximations provide useful numerical tools to compute fractional derivatives of functions. Application of such approximations to fractional differential equations and fractional problems of the calculus of variations are discussed. Illustrative examples show the advantages and disadvantages of each approximation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-08-13T13:49:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26A33",
      "33F05",
      "34A08",
      "49M99",
      "65D20"
    ],
    "keywords": [
      "numerical approximations",
      "application",
      "fractional differential equations",
      "riemann-liouville fractional derivatives",
      "integer order derivatives"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1208.2588P"
    }
  }
}