{
  "id": "2007.10128",
  "version": "v1",
  "published": "2020-07-15T23:36:55.000Z",
  "updated": "2020-07-15T23:36:55.000Z",
  "title": "Existence and Uniqueness Results for a nonlinear fractional differential equations of order $σ\\in(1,2)$",
  "authors": [
    "S. S. Bilgici",
    "M. Şan"
  ],
  "comment": "13 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "The main objective of this article is to discuss the local existence of the solution to an initial value problem involving a non-linear differential equation in the sense of Riemann-Liouville fractional derivative of order $\\sigma\\in(1,2),$ when the nonlinear term has a discontinuity at zero. Hereafter, by using some tools of Lebesgue spaces such as H\\\"older inequality, we obtain Nagumo-type, Krasnoselskii-Krein-type and Osgood-type uniqueness theorems for the problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-15T23:36:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34A08",
      "37C25",
      "34A12",
      "74G20",
      "26A33"
    ],
    "keywords": [
      "nonlinear fractional differential equations",
      "uniqueness results",
      "initial value problem",
      "non-linear differential equation",
      "osgood-type uniqueness theorems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}