{
  "abstract": "We study front propagation in a time-fractional Amari neural field equation with a Caputo derivative and a Heaviside firing-rate function. For a class of nonnegative even connectivity kernels and strictly decreasing $C^1$ front-like initial data, we reduce the Cauchy problem to a nonlinear Volterra equation for the threshold location. We prove the existence and uniqueness of a global front solution, determine the short-time behavior of its threshold location, and identify its asymptotic speed. We also construct the associated asymptotic traveling-wave profile and establish uniqueness of the speed and profile, up to translation, in the nonzero-speed case. Using a rigidity argument, we prove the asymptotic linearity of the local increments of the threshold location and obtain uniform convergence to the profile in the threshold-centered frame. Finally, we characterize the kernel-dependent tail asymptotics of the wave profile.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14884",
  "author_total": 1,
  "authors": [
    {
      "name": "Hiroshi Ishii"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0126rpnq434hx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14884",
  "fulltext_url": null,
  "id": "0126rpnq434hx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14884",
  "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": "W7213360588",
  "pdf_url": "https://arxiv.org/pdf/2609.14884",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0126rpnq434hx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:45Z",
      "native_id": "2609.14884",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14884"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Global front solutions converging to an asymptotic traveling wave in a time-fractional Amari model",
  "title_text": "Global front solutions converging to an asymptotic traveling wave in a time-fractional Amari model",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:45Z",
  "url": "https://research.draconitic.com/paper/0126rpnq434hx",
  "venue": "arXiv",
  "versions": []
}