{
  "abstract": "This study investigates the algebraic and differential properties of balancing-like polynomials, which constitute a polynomial extension of balancing-like sequences. Several fundamental properties are established, including matrix representations, addition and subtraction formulas, and polynomial analogues of the Cassini, Catalan, D’Ocagne, and Vajda identities. A product factorization is obtained, which yields an explicit description of the zeros of these polynomials. Moreover, a direct connection with the Chebyshev polynomials of the second kind is established, and the ordinary generating function of the balancing-like polynomials is derived. The derivative sequences associated with these polynomials are then systematically investigated. Explicit formulas, recurrence relations, and a self-convolution identity are obtained, together with a relation recovering the original polynomials from their neighboring derivative terms. Finally, the analysis is extended to higher-order derivatives, and a generating-function representation and a general recurrence relation for the resulting differential hierarchy are derived. The differential framework is further extended to non-integer orders by means of the Caputo fractional derivative. An explicit fractional derivative formula and a generating-function representation are obtained.",
  "abstract_shown": true,
  "affiliations": [
    "Department of Mathematics, Faculty of Science, Marmara University, Istanbul 34722, Türkiye"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Engin Özkan",
      "orcid": "0000-0002-4188-7248"
    },
    {
      "affs": [
        0
      ],
      "name": "Beyza Tekeoğlu Akkaya",
      "orcid": "0009-0005-7985-8951"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4f5ja78r1xa7j.bib",
  "cited_by": 0,
  "doi": "10.3390/fractalfract10100732",
  "fulltext_url": null,
  "id": "4f5ja78r1xa7j",
  "issns": [
    "2504-3110"
  ],
  "landing_url": "https://www.mdpi.com/2504-3110/10/10/732",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2604|Mathematical functions and polynomials"
    ]
  ],
  "openalex": "W7223187027",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/4f5ja78r1xa7j.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:32Z",
      "native_id": "10.3390/fractalfract10100732",
      "source": "crossref",
      "url": "https://www.mdpi.com/2504-3110/10/10/732"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "issn:2504-3110",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Algebraic, Differential and Fractional Properties of Balancing-like Polynomials",
  "title_text": "Algebraic, Differential and Fractional Properties of Balancing-like Polynomials",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:32Z",
  "url": "https://research.draconitic.com/paper/4f5ja78r1xa7j",
  "venue": "Fractal and Fractional",
  "versions": []
}