{
  "abstract": "We prove a representation theorem for finite series-parallel viscoelastic networks composed of springs and spring-pots of a common order $0<α<1$. The associated complex shear modulus, expressed in an appropriately chosen auxiliary variable, is rational and admits a finite partial-fraction representation with simple poles on the negative real axis and negative residues. Its reciprocal admits an analogous representation with positive residues and a possible additional pole at the origin. Inverting the corresponding Laplace transforms gives finite fractional Prony representations of the relaxation modulus and creep compliance with non-negative amplitudes. These results provide a rigorous proof of a corrected version of the Mainardi-Spada conjecture for this network class. A six-element network illustrates the construction.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.00750",
  "author_total": 4,
  "authors": [
    {
      "name": "Andrea Giusti"
    },
    {
      "name": "Ivano Colombaro"
    },
    {
      "name": "Andrea Mentrelli"
    },
    {
      "name": "Francesco Mainardi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ecyvb4dqqddp6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.00750",
  "fulltext_url": null,
  "id": "ecyvb4dqqddp6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.00750",
  "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-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.00750",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ecyvb4dqqddp6.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:20:59Z",
      "native_id": "2611.00750",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.00750"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "A Representation Theorem for Fractional Viscoelastic Networks",
  "title_text": "A Representation Theorem for Fractional Viscoelastic Networks",
  "type": "preprint",
  "updated_at": "2026-11-04T15:21:05Z",
  "url": "https://research.draconitic.com/paper/ecyvb4dqqddp6",
  "venue": "arXiv",
  "versions": []
}