{
  "id": "2303.10669",
  "version": "v1",
  "published": "2023-03-19T14:17:49.000Z",
  "updated": "2023-03-19T14:17:49.000Z",
  "title": "Inverse problem of determining the order of the fractional derivative in the Rayleigh-Stokes equation",
  "authors": [
    "Ravshan Ashurov",
    "Oqila Mukhiddinova"
  ],
  "comment": "Inverse problem of determining the order of the fractional derivative in the Rayleigh-Stokes equation",
  "categories": [
    "math.AP"
  ],
  "abstract": "In recent years, much attention has been paid to the study of forward and inverse problems for the Rayleigh-Stokes equation in connection with the importance of this equation for applications. This equation plays an important role, in particular, in the study of the behavior of certain non-Newtonian fluids. The equation includes a fractional derivative of order $\\alpha$, which is used to describe the viscoelastic behavior of the flow. In this paper, we study the behavior of the solution of such equations depending on the parameter $\\alpha$. In particular, it is proved that for sufficiently large $t$ the norm $||u(x,t)||_{L_2(\\Omega)}$ of the solution decreases with respect to $\\alpha$. Moreover the inverse problem of determining the order of the derivative $\\alpha$ is solved uniquely.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-03-19T14:17:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "inverse problem",
      "rayleigh-stokes equation",
      "fractional derivative",
      "determining",
      "equation plays"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}