{
  "id": "2212.11794",
  "version": "v1",
  "published": "2022-12-06T07:45:17.000Z",
  "updated": "2022-12-06T07:45:17.000Z",
  "title": "Analytical solutions of moving boundary problems for the time-fractional diffusion equation",
  "authors": [
    "M. Rodrigo"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "The time-fractional diffusion equation is considered, where the time derivative is either of Caputo or Riemann-Liouville type. The solution of a general initial-boundary value problem with time-dependent boundary conditions over bounded and unbounded domains is derived using the embedding method. The solution of the initial-boundary value problem, expressed in terms of a two-parameter auxiliary function, is used to obtain analytical solutions of moving boundary problems. In particular, a 'fractional' analogue of the Neumann solution to a classical Stefan problem for melting ice is found.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-06T07:45:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26A33",
      "35R11",
      "35K05"
    ],
    "keywords": [
      "time-fractional diffusion equation",
      "moving boundary problems",
      "analytical solutions",
      "general initial-boundary value problem",
      "two-parameter auxiliary function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}