{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:44:07Z","timestamp":1760060647393,"version":"build-2065373602"},"reference-count":38,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2025,9,21]],"date-time":"2025-09-21T00:00:00Z","timestamp":1758412800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, we introduce and investigate a new subclass R\u03c2ug(\u03d5) of universally prestarlike generalized functions of order \u03c2, where \u03c2\u22641, associated with a shell-shaped region defined by \u039b=C\u2216[1,\u221e) for the present investigation, by utilizing the Srivastava\u2013Owa fractional derivative of order \u03b4. Coefficient inequalities for |a2| and |a3| for functions belonging to the newly introduced class are obtained. Additionally, the Fekete\u2013Szeg\u00f6 inequality is investigated for this class of functions. In order to enhance the coefficient studies for this class, the second Hankel determinant is also evaluated.<\/jats:p>","DOI":"10.3390\/axioms14090711","type":"journal-article","created":{"date-parts":[[2025,9,22]],"date-time":"2025-09-22T12:08:03Z","timestamp":1758542883000},"page":"711","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Coefficient Estimates, the Fekete\u2013Szeg\u00f6 Inequality, and Hankel Determinants for Universally Prestarlike Functions Defined by Fractional Derivative in a Shell-Shaped Region"],"prefix":"10.3390","volume":"14","author":[{"given":"Dina","family":"Nabil","sequence":"first","affiliation":[{"name":"Department of Mathematics, University Mansoura, Mansoura 35516, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2902-4455","authenticated-orcid":false,"given":"Georgia Irina","family":"Oros","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, University of Oradea, 410087 Oradea, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Awatef","family":"Shahin","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University Mansoura, Mansoura 35516, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hanan","family":"Darwish","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University Mansoura, Mansoura 35516, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,9,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"808","DOI":"10.1016\/j.jmaa.2011.07.014","article-title":"Starlikeness of integral transforms and duality","volume":"385","author":"Ali","year":"2012","journal-title":"J. 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