{
  "abstract": "Given a fractional-order linear equation $L^αu = f$, we define an appropriate symmetric bilinear form so that the fractional operator $L^α$ is symmetric with respect to that bilinear form. Using the bilinear form, we then define a functional of the fractional calculus of variations proving that the solutions of the given fractional-order equation are critical points of the fractional variational functional. In the case of fractional integral equations, the provided bilinear form is non-degenerate, and all critical points are solutions of the given equation. In the case of fractional differential equations, a relation with the least-squares method is obtained.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: J. Convex Anal. 34 (2027), no. 1, 582--590",
  "arxiv": "2607.22659",
  "author_total": 1,
  "authors": [
    {
      "name": "Delfim F. M. Torres"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e8s5hwwx5bp98.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.22659",
  "fulltext_url": null,
  "id": "e8s5hwwx5bp98",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.22659",
  "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.OC"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2607.22659",
  "pmcid": null,
  "pmid": null,
  "published": "2026-07-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e8s5hwwx5bp98.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2607.22659",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.22659"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Variational Formulations for Fractional Integral and Differential Equations",
  "title_text": "Variational Formulations for Fractional Integral and Differential Equations",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:25Z",
  "url": "https://research.draconitic.com/paper/e8s5hwwx5bp98",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.68381/jca34039",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}