{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,5]],"date-time":"2026-03-05T04:28:49Z","timestamp":1772684929143,"version":"3.50.1"},"reference-count":38,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,1,28]],"date-time":"2023-01-28T00:00:00Z","timestamp":1674864000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"University of Oradea"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Sanford S. Miller and Petru T. Mocanu\u2019s theory of second-order differential subordinations was extended for the case of third-order differential subordinations by Jos\u00e9 A. Antonino and Sanford S. Miller in 2011. In this paper, new results are proved regarding third-order differential subordinations that extend the ones involving the classical second-order differential subordination theory. A method for finding a dominant of a third-order differential subordination is provided when the behavior of the function is not known on the boundary of the unit disc. Additionally, a new method for obtaining the best dominant of a third-order differential subordination is presented. This newly proposed method essentially consists of finding the univalent solution for the differential equation that corresponds to the differential subordination considered in the investigation; previous results involving third-order differential subordinations have been obtained mainly by investigating specific classes of admissible functions. The fractional integral of the Gaussian hypergeometric function, previously associated with the theory of fuzzy differential subordination, is used in this paper to obtain an interesting third-order differential subordination by involving a specific convex function. The best dominant is also provided, and the example presented proves the importance of the theoretical results involving the fractional integral of the Gaussian hypergeometric function.<\/jats:p>","DOI":"10.3390\/axioms12020133","type":"journal-article","created":{"date-parts":[[2023,1,30]],"date-time":"2023-01-30T02:01:18Z","timestamp":1675044078000},"page":"133","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Third-Order Differential Subordinations Using Fractional Integral of Gaussian Hypergeometric Function"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2902-4455","authenticated-orcid":false,"given":"Georgia Irina","family":"Oros","sequence":"first","affiliation":[{"name":"Department of Mathematics and Computer Science, Faculty of Informatics and Sciences, University of Oradea, 410087 Oradea, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1000-094X","authenticated-orcid":false,"given":"Gheorghe","family":"Oros","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, Faculty of Informatics and Sciences, University of Oradea, 410087 Oradea, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9215-2404","authenticated-orcid":false,"given":"Lavinia Florina","family":"Preluca","sequence":"additional","affiliation":[{"name":"Doctoral School of Engineering Sciences, University of Oradea, 410087 Oradea, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"298","DOI":"10.1016\/0022-247X(78)90181-6","article-title":"Second order-differential inequalities in the complex plane","volume":"65","author":"Miller","year":"1978","journal-title":"J. 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