{
  "id": "1710.03712",
  "version": "v1",
  "published": "2017-10-10T16:36:09.000Z",
  "updated": "2017-10-10T16:36:09.000Z",
  "title": "On two new operators in fractional calculus and application",
  "authors": [
    "J. Vanterler da C. Sousa",
    "E. Capelas de Oliveira"
  ],
  "comment": "17 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "Motivated by the fractional derivative $\\psi$-Riemann-Liouville and by the fractional derivative $\\psi$-Hilfer, we introduced two new fractional operators: $\\psi$-fractional integral and $\\psi$-fractional derivative. We present and discuss relationships between these the two fractional operators, as well as, we guarantee that the $\\psi$-fractional integration operator is limited. In this sense, we present some examples, in particular, that involve the Mittag-Leffler function, of paramount importance in the solution of population growth problem, as approached.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-10T16:36:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fractional calculus",
      "application",
      "fractional derivative",
      "fractional operators",
      "population growth problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}