{
  "abstract": "We consider an initial value problem for a time-fractional evolution equation in a Hilbert space $X$: $$ \\partial_t^α (u(t)-a) = Au(t) \\qquad \\mbox{for $0<t<T$}, $$ where $\\partial_t^α$ denotes a fractional differential operator of Caputo type with order $0<α<1,$ $u\\colon (0,T) \\to X,$ $a$ describes an initial value, and $A$, with domain $\\mathcal{D}(A),$ is the generator of a contraction C$_0$ semigroup in $X$. We prove a fractional Hille-Yosida theorem characterizing the unique existence of a weak solution for every $a\\in X$. We also discuss the unique existence of a strong solution for $a \\in \\mathcal{D}(A),$ as well as the continuity of weak solutions. Our results are applicable, for example, to time-fractional transport equations and Boltzmann equations. The proofs are mainly based on constructing an approximating sequence of solutions using the Yosida approximation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.35001",
  "author_total": 3,
  "authors": [
    {
      "name": "S. E. Chorfi"
    },
    {
      "name": "F. Gölgeleyen"
    },
    {
      "name": "M. Yamamoto"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ac0zabmbmg6c5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.35001",
  "fulltext_url": null,
  "id": "ac0zabmbmg6c5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.35001",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "2604|Nonlinear Differential Equations Analysis"
    ]
  ],
  "openalex": "W7214733444",
  "pdf_url": "https://arxiv.org/pdf/2609.35001",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ac0zabmbmg6c5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.35001",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.35001"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Well-posedness for time-fractional evolution equations by the Yosida approximation",
  "title_text": "Well-posedness for time-fractional evolution equations by the Yosida approximation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/ac0zabmbmg6c5",
  "venue": "arXiv",
  "versions": []
}