{
  "abstract": "In this paper, we use a normalized fractional q-derivative operator, constructed by combining Jackson’s q-difference operator with a fractional q-integral, to introduce two subclasses of normalized analytic functions in the open unit disk whose fractional transforms are starlike and univalent. The first subclass, Sq,λ*(ML), is defined by subordination to a normalized q-Mittag–Leffler function, whereas the second, Sq,λ*(L), is associated with a generalized limaçon domain. For both classes, we investigate sharp initial coefficient bounds and sharp estimates for the Fekete–Szegö functional. We also study inclusion and radius relations between the two classes. This comparative approach clarifies how an analytically defined Mittag–Leffler domain and a geometrically defined limaçon domain affect coefficient estimates when the underlying operator is held fixed. Relevant classical and quantum calculus results are recovered through suitable parameter choices and in the limiting case q→1−.",
  "abstract_shown": true,
  "affiliations": [
    "Department of Mathematics, Faculty of Science, Jazan University, Jazan 45142, Saudi Arabia",
    "Department of Management Information Systems, College of Business and Economics, Qassim University, Buraydah 51452, Saudi Arabia",
    "Department of Mathematics, Abdul Wali Khan University Mardan, Mardan 23200, Pakistan"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 5,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Hussain Gissy",
      "orcid": "0000-0001-7869-7731"
    },
    {
      "affs": [
        1
      ],
      "name": "Mohamed Biomy",
      "orcid": "0000-0002-6769-0881"
    },
    {
      "affs": [
        2
      ],
      "name": "Mirajul Haq"
    },
    {
      "affs": [
        2
      ],
      "name": "Muhammad Arif",
      "orcid": "0000-0003-1484-7643"
    },
    {
      "affs": [
        2
      ],
      "name": "Muhammad Abbas",
      "orcid": "0009-0001-9962-2146"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9rpfv4n8dp4dz.bib",
  "cited_by": 0,
  "doi": "10.3390/fractalfract10100720",
  "fulltext_url": null,
  "id": "9rpfv4n8dp4dz",
  "issns": [
    "2504-3110"
  ],
  "landing_url": "https://www.mdpi.com/2504-3110/10/10/720",
  "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",
      "2608|Analytic and geometric function theory"
    ]
  ],
  "openalex": "W7221754200",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/9rpfv4n8dp4dz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:32Z",
      "native_id": "10.3390/fractalfract10100720",
      "source": "crossref",
      "url": "https://www.mdpi.com/2504-3110/10/10/720"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2608|Analytic and geometric function theory",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Fractional q-Starlikeness in Mittag–Leffler and Limaçon Domains",
  "title_text": "Fractional q-Starlikeness in Mittag–Leffler and Limaçon Domains",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:32Z",
  "url": "https://research.draconitic.com/paper/9rpfv4n8dp4dz",
  "venue": "Fractal and Fractional",
  "versions": []
}