{
  "id": "1606.04844",
  "version": "v1",
  "published": "2016-06-11T00:43:47.000Z",
  "updated": "2016-06-11T00:43:47.000Z",
  "title": "Fractional derivative with non-singular kernels in anomalous relaxation and diffusion modeling",
  "authors": [
    "HongGuang Sun",
    "Xiaoxiao Hao",
    "Yong Zhang",
    "Dumitru Baleanu"
  ],
  "comment": "16 pages, 5 figures",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "Anomalous relaxation and diffusion processes are major application area of fractional derivative models. This paper offers an investigation on physical behavior of fractional derivative relaxation and diffusion models by using a new definition of fractional derivative with exponential kernel. Our analytical results indicate that the fractional derivative models with new definition cannot well characterize non-exponential nature of anomalous relaxation and diffusion processes. Hereby, this paper introduces a legitimate extension of fractional derivative by replacing exponential kernel with a stretched exponential kernel. Numerical results illustrate the fractional derivative model with stretched exponential kernel can describe wide range of anomalous physical phenomena, compared with the exponential kernel.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-11T00:43:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "anomalous relaxation",
      "fractional derivative model",
      "non-singular kernels",
      "diffusion modeling",
      "stretched exponential kernel"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}