{
  "id": "2402.13691",
  "version": "v2",
  "published": "2024-02-21T10:52:27.000Z",
  "updated": "2024-11-12T17:56:00.000Z",
  "title": "Higher-order fractional equations and related time-changed pseudo-processes",
  "authors": [
    "Fabrizio Cinque",
    "Enzo Orsingher"
  ],
  "comment": "21",
  "categories": [
    "math.PR"
  ],
  "abstract": "We study Cauchy problems of fractional differential equations in both space and time variables by expressing the solution in terms of ``stochastic composition\" of the solutions to two simpler problems. These Cauchy sub-problems respectively concern the space and the time differential operator involved in the main equation. We provide some probabilistic and pseudo-probabilistic applications, where the solution can be interpreted as the pseudo-transition density of a time-changed pseudo-process. To extend our results to higher order time-fractional problems, we introduce pseudo-subordinators as well as its pseudo-inverse. Finally, we present our results in the case of more general differential operators and we interpret the results by means of a linear combination of pseudo-subordinators and its inverse.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2024-11-12T17:56:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R11",
      "60K99"
    ],
    "keywords": [
      "higher-order fractional equations",
      "related time-changed pseudo-processes",
      "higher order time-fractional problems",
      "fractional differential equations",
      "general differential operators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}