{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T13:31:11Z","timestamp":1776778271582,"version":"3.51.2"},"reference-count":39,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2021,6,7]],"date-time":"2021-06-07T00:00:00Z","timestamp":1623024000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, we investigate several fuzzy differential subordinations that are connected with the Borel distribution series B\u03bb,\u03b1,\u03b2(z) of the Mittag-Leffler type, which involves the two-parameter Mittag-Leffler function E\u03b1,\u03b2(z). Using the above-mentioned operator B\u03bb,\u03b1,\u03b2, we also introduce and study a class M\u03bb,\u03b1,\u03b2F\u03b7 of holomorphic and univalent functions in the open unit disk \u0394. The Mittag-Leffler-type functions, which we have used in the present investigation, belong to the significantly wider family of the Fox-Wright function p\u03a8q(z), whose p numerator parameters and q denominator parameters possess a kind of symmetry behavior in the sense that it remains invariant (or unchanged) when the order of the p numerator parameters or when the order of the q denominator parameters is arbitrarily changed. Here, in this article, we have used such special functions in our study of a general Borel-type probability distribution, which may be symmetric or asymmetric. As symmetry is generally present in most works involving fuzzy sets and fuzzy systems, our usages here of fuzzy subordinations and fuzzy membership functions potentially possess local or non-local symmetry features.<\/jats:p>","DOI":"10.3390\/sym13061023","type":"journal-article","created":{"date-parts":[[2021,6,7]],"date-time":"2021-06-07T22:23:00Z","timestamp":1623104580000},"page":"1023","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":51,"title":["Fuzzy Differential Subordinations Based upon the Mittag-Leffler Type Borel Distribution"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9277-8092","authenticated-orcid":false,"given":"Hari Mohan","family":"Srivastava","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada"},{"name":"Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan"},{"name":"Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, Baku AZ1007, Azerbaijan"},{"name":"Section of Mathematics, International Telematic University Uninettuno, I-00186 Rome, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4052-391X","authenticated-orcid":false,"given":"Sheza M.","family":"El-Deeb","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science and Arts in Al-Badaya, Qassim University, Buraidah 51911, Saudi Arabia"},{"name":"Department of Mathematics, Faculty of Science, Damietta University, New Damietta 34517, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,6,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"235","DOI":"10.22436\/jmcs.024.03.05","article-title":"Bi-Bazilevi\u010d functions based on the Mittag-Leffler-type Borel distribution associated with Legendre polynomials","volume":"24","author":"Murugusundaramoorthy","year":"2021","journal-title":"J. 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