{
  "id": "2308.01232",
  "version": "v1",
  "published": "2023-08-02T15:39:26.000Z",
  "updated": "2023-08-02T15:39:26.000Z",
  "title": "One inverse source problem generated by the Dunkl operator",
  "authors": [
    "Bayan Bekbolat",
    "Niyaz Tokmagambetov"
  ],
  "comment": "20 pages, 2 figures",
  "categories": [
    "math.AP"
  ],
  "abstract": "The aim of this paper is to study time-fractional pseudo-parabolic type equations generated by the Dunkl operator. The forward problem is considered and its well-posedness is established. In particular, a prior estimates are obtained in the Sobolev type spaces and, explicit formulas for solutions of the problems are derived. Here we also deal with the left-sided Caputo fractional time derivative. As an application, we investigate an inverse source problem. Existence and uniqueness of the solution is proved. Moreover, we show that a solution pair is continuously depending on the initial and additional data, finalizing with a numerical test.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-02T15:39:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R30",
      "35R11",
      "35C15"
    ],
    "keywords": [
      "inverse source problem",
      "dunkl operator",
      "caputo fractional time derivative",
      "study time-fractional pseudo-parabolic type equations",
      "sobolev type spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}