{
  "abstract": "We develop a contour-based method for applying Riemann--Liouville fractional integrals in a Jacobi fractional polynomial basis with an endpoint weight. A Gamma-ratio representation reduces the action to contour quadrature and banded ultraspherical solves. For a fixed number of contour nodes, the cost and storage are linear in the polynomial dimension. For fractional equations, we construct selected diagonals of a short rational approximation directly and use their banded factorizations as reusable right preconditioners for Krylov iterations. Numerical experiments show accurate integral actions and substantially reduced solution costs across Abel, multi-order, BBO, deferred-correction, eigenvalue, and boundary-value problems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.39388",
  "author_total": 1,
  "authors": [
    {
      "name": "Xiaolin Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bh44e2nmrerr4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.39388",
  "fulltext_url": null,
  "id": "bh44e2nmrerr4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.39388",
  "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",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.39388",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bh44e2nmrerr4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.39388",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.39388"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Contour-Based Fast Fractional Integration in a Jacobi Fractional Polynomial Basis",
  "title_text": "Contour-Based Fast Fractional Integration in a Jacobi Fractional Polynomial Basis",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/bh44e2nmrerr4",
  "venue": "arXiv",
  "versions": []
}