{
  "abstract": "The gelation transition, a process that transforms a flowable liquid into an elastic solid, occurs in a variety of systems, ranging from colloidal to polymeric. During the gelation transition, a system passes through a critical gel state characterized by scale-free power-law viscoelasticity. Interestingly, the fractional calculus provides a natural mathematical language for such power-law viscoelasticity. In this work, we develop physically constrained fractional viscoelastic models, as well as those based on the three-parameter Mittag-Leffler-Prabhakar function, for both the pre-gel and post-gel regimes, ensuring consistency with the conventional scaling relations in each regime. While the fractional pre-gel model is observed to be valid only for a restricted subset of parameter values, the Prabhakar function-based model for the relaxation modulus, which translates into a Havriliak-Negami function-based complex modulus, rigorously removes this limitation. We enforce continuity of the dynamic moduli and their derivatives across the critical gel point, which universally imposes a symmetry in the relaxation dynamics on either side of the critical gel state. Such enforcement further validates the hyperscaling relation connecting the critical exponents, making it a theoretical necessity rather than an empirical coincidence. We validate the proposed models against time- and frequency-domain experimental data. A model-agnostic, frequency-independent rheological fingerprint of the critical gel state, uniquely determined by two critical exponents, is also identified.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.26656",
  "author_total": 1,
  "authors": [
    {
      "name": "Yogesh M Joshi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1kkvb66q28dpk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.26656",
  "fulltext_url": null,
  "id": "1kkvb66q28dpk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.26656",
  "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",
      "cond-mat.soft"
    ],
    [
      "openalex",
      "2611|Fractional Differential Equations Solutions"
    ]
  ],
  "openalex": "W7166197907",
  "pdf_url": "https://arxiv.org/pdf/2606.26656",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1kkvb66q28dpk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:15Z",
      "native_id": "2606.26656",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.26656"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.soft",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Analyzing the Gelation Transition through Fractional Viscoelasticity and the Mittag-Leffler-Prabhakar Function",
  "title_text": "Analyzing the Gelation Transition through Fractional Viscoelasticity and the Mittag-Leffler-Prabhakar Function",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:15Z",
  "url": "https://research.draconitic.com/paper/1kkvb66q28dpk",
  "venue": "arXiv",
  "versions": []
}