{
  "abstract": "We prove the existence of a McKean--Vlasov stochastic process with jumps associated to the nonlinear parabolic equation $\\partial_t u = Δ_p u + Δ_p^s u$ in $\\mathbb{R}^N\\times(0,\\infty)$, where $Δ_p$ is the $p$-Laplacian and $Δ_p^s$ is the fractional $p$-Laplacian. Our approach is the following: first, after proving the existence of a solution for the PDE presented earlier, we rewrite it as a nonlinear Fokker-Planck-Kolmogorov equation whose measure-valued solution is guaranteed when $p\\ge4$. Then we solve the martingale problem associated to our FPKE via a new superposition principle for non-local Fokker-Planck-Kolmogorov equations, which only requires an integrability condition on the local coefficients. Finally, thanks to the martingale solution obtained, we derive the existence of a weak solution for the McKean-Vlasov's type SDE with jumps whose infinitesimal generator is a << hybrid version >> of the operator $Δ_p+Δ_p^s$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.19492",
  "author_total": 2,
  "authors": [
    {
      "name": "Houssine El Jeddaoui"
    },
    {
      "name": "Dany Nabab"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/90py4fmrdqz6b.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.19492",
  "fulltext_url": null,
  "id": "90py4fmrdqz6b",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.19492",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7213600329",
  "pdf_url": "https://arxiv.org/pdf/2609.19492",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/90py4fmrdqz6b.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2609.19492",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.19492"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "New link between the fractional p-Laplacian operators and a class of McKean-Vlasov flight type processes",
  "title_text": "New link between the fractional p-Laplacian operators and a class of McKean-Vlasov flight type processes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/90py4fmrdqz6b",
  "venue": "arXiv",
  "versions": []
}