{
  "abstract": "We establish the existence and uniqueness of solutions to a $(1+1)$-dimensional fractional stochastic Burgers-type equation featuring a Caputo fractional time derivative, a fractional Laplacian, and space-time white noise forcing modified by a Riemann-Liouville fractional integral. From a physical perspective, equations of this type describe non-Markovian dynamics with long-range temporal and spatial dependencies. The main difficulty is that the solution to the linearized equation has low spatial Hölder regularity, rendering the singular nonlinearity $G(u)\\partial_x u$ classically ill-defined. The proof relies on two main ingredients: first, combining the Da Prato-Debussche decomposition with rough path theory to rigorously interpret the nonlinear product; and second, deriving Schauder-type estimates for fractional heat kernels given in terms of slowly decaying Mittag-Leffler functions. The nonlocality of the fractional time derivative requires a strong assumption on the initial condition.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.20599",
  "author_total": 2,
  "authors": [
    {
      "name": "Ming-Wei Kuo"
    },
    {
      "name": "Konstantin Matetski"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ezn3gyabgyswg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.20599",
  "fulltext_url": null,
  "id": "ezn3gyabgyswg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.20599",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2611|Fractional Differential Equations Solutions"
    ]
  ],
  "openalex": "W7213585499",
  "pdf_url": "https://arxiv.org/pdf/2609.20599",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ezn3gyabgyswg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.20599",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.20599"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Space-time fractional stochastic Burgers-type equation",
  "title_text": "Space-time fractional stochastic Burgers-type equation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/ezn3gyabgyswg",
  "venue": "arXiv",
  "versions": []
}