{
  "id": "1801.08904",
  "version": "v1",
  "published": "2018-01-26T17:27:58.000Z",
  "updated": "2018-01-26T17:27:58.000Z",
  "title": "Maximum principle and its application for the nonlinear time-fractional diffusion equations with Cauchy-Dirichlet conditions",
  "authors": [
    "Meiirkhan Borikhanov",
    "Mokhtar Kirane",
    "Berikbol T. Torebek"
  ],
  "comment": "to appear in Applied Mathematics Letters",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, a maximum principle for the one-dimensional sub-diffusion equation with Atangana-Baleanu fractional derivative is formulated and proved. The proof of the maximum principle is based on an extremum principle for the Atangana-Baleanu fractional derivative that is given in the paper, too. The maximum principle is then applied to show that the initial-boundary-value problem for the linear and nonlinear time-fractional diffusion equations possesses at most one classical solution and this solution continuously depends on the initial and boundary conditions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-26T17:27:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26A33"
    ],
    "keywords": [
      "maximum principle",
      "cauchy-dirichlet conditions",
      "nonlinear time-fractional diffusion equations possesses",
      "application",
      "atangana-baleanu fractional derivative"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}