{
  "abstract": "We consider the recovery of the fractional order in a time-fractional evolution equation with a source of the form $p(t)f$, where the temporal factor $p$ is also unknown but belongs to a bounded admissible class and has a prescribed nonzero value at $t=0$. From one scalar observation we prove a uniform small-time expansion and obtain a Hölder estimate for the fractional order. More precisely, if a fixed derivative order $γ$ lies below every admissible fractional order, then the stability exponent is $α_+/(2α_+-γ)$; for the undifferentiated observation this gives the exponent $1/2$. We also show that differentiating the data to an order larger than all admissible fractional orders is supercritical: the corresponding derivative is unbounded near $t=0$ whenever the two fractional orders are different. A uniform estimate for the two-parameter Mittag--Leffler function, including the diagonal case, is proved in the appendix.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.30799",
  "author_total": 2,
  "authors": [
    {
      "name": "Ravshan Ashurov"
    },
    {
      "name": "Masahiro Yamamoto"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1byrg90qms21y.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.30799",
  "fulltext_url": null,
  "id": "1byrg90qms21y",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.30799",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2610|Numerical methods in inverse problems"
    ]
  ],
  "openalex": "W7214643421",
  "pdf_url": "https://arxiv.org/pdf/2609.30799",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1byrg90qms21y.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:57Z",
      "native_id": "2609.30799",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.30799"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Stability in recovering the order of a time-fractional evolution equation",
  "title_text": "Stability in recovering the order of a time-fractional evolution equation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:57Z",
  "url": "https://research.draconitic.com/paper/1byrg90qms21y",
  "venue": "arXiv",
  "versions": []
}