{
  "abstract": "In this work, we study a fractional diffusion model in time and space, formulated in an open and bounded domain, involving a Caputo fractional derivative of order $μ\\in(0,1)$ with respect to a time scale function $Ψ$, together with a spectral fractional Laplacian operator of order $s\\in(0,1)$. The associated direct problem is analyzed, as well as the inverse problem of temporal reconstruction from final data, which is inherently ill-posed. Through a spectral representation, the instability of the problem and the effect of the choice of the function $Ψ$ on the amplification of spectral modes are examined.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.28463",
  "author_total": 2,
  "authors": [
    {
      "name": "Nelson R. Ojeda"
    },
    {
      "name": "Ruben D. Spies"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6chwrev8gcdyh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.28463",
  "fulltext_url": null,
  "id": "6chwrev8gcdyh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.28463",
  "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",
      "2611|Fractional Differential Equations Solutions"
    ]
  ],
  "openalex": "W7223099233",
  "pdf_url": "https://arxiv.org/pdf/2610.28463",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6chwrev8gcdyh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.28463",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.28463"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Backward Homogeneous Heat Equation with $Ψ$-Caputo Time Derivative and Spectral Fractional Laplacian",
  "title_text": "Backward Homogeneous Heat Equation with Ψ-Caputo Time Derivative and Spectral Fractional Laplacian",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/6chwrev8gcdyh",
  "venue": "arXiv",
  "versions": []
}