{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,2]],"date-time":"2025-11-02T09:41:39Z","timestamp":1762076499847,"version":"build-2065373602"},"reference-count":13,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2022,11,18]],"date-time":"2022-11-18T00:00:00Z","timestamp":1668729600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Saudi Electronic University, Riyadh-11673, Saudi Arabia","award":["FRGS\/1\/2019\/STG06\/UKM\/01\/"],"award-info":[{"award-number":["FRGS\/1\/2019\/STG06\/UKM\/01\/"]}]},{"name":"UKM","award":["FRGS\/1\/2019\/STG06\/UKM\/01\/"],"award-info":[{"award-number":["FRGS\/1\/2019\/STG06\/UKM\/01\/"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Fractional calculus has a number of applications in the field of science, specially in mathematics. In this paper, we discuss some applications of fractional differential operators in the field of geometric function theory. Here, we combine the fractional differential operator and the Mittag-Leffler functions to formulate and arrange a new operator of fractional calculus. We define a new class of normalized analytic functions by means of a newly defined fractional operator and discuss some of its interesting geometric properties in open unit disk.<\/jats:p>","DOI":"10.3390\/axioms11110655","type":"journal-article","created":{"date-parts":[[2022,11,21]],"date-time":"2022-11-21T04:33:32Z","timestamp":1669005212000},"page":"655","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Certain New Class of Analytic Functions Defined by Using a Fractional Derivative and Mittag-Leffler Functions"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5053-5028","authenticated-orcid":false,"given":"Mohammad Faisal","family":"Khan","sequence":"first","affiliation":[{"name":"Department of Basic Science, College of Science and Theoretical Studies, Saudi Electronic University, Riyadh 11673, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0361-4887","authenticated-orcid":false,"given":"Shahid","family":"Khan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad 22500, Pakistan"}]},{"given":"Saqib","family":"Hussain","sequence":"additional","affiliation":[{"name":"Department of Mathematics, COMSATS University, Abbottabad Campus, Abbottabad 22060, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9138-916X","authenticated-orcid":false,"given":"Maslina","family":"Darus","sequence":"additional","affiliation":[{"name":"Department of Mathematical Science, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi 43600, Malaysia"}]},{"given":"Khaled","family":"Matarneh","sequence":"additional","affiliation":[{"name":"Faculity of Computer Science, Arab Open University, Riyadh 11681, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,18]]},"reference":[{"key":"ref_1","unstructured":"Goodman, A.W. (1983). Univalent Functions, Polygonal Publishing House."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"420","DOI":"10.4153\/CJM-1973-042-6","article-title":"Majorization-subordination theorems for locally univalent functions, II","volume":"25","author":"Campbell","year":"1973","journal-title":"Can. J. Math."},{"key":"ref_3","unstructured":"Srivastava, H.M., and Owa, S. (1989). Univalent functions, fractional calculus, and associated generalized hypergeometric functions. Univalent Functions, Fractional Calculus, and Their Applications, John Wiley & Sons."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1186\/1687-1847-2011-55","article-title":"On generalized Srivastava-Owa fractional operators in the unit disk","volume":"2011","author":"Ibrahim","year":"2011","journal-title":"Adv. Differ. 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Sci."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"362","DOI":"10.1007\/BFb0066543","article-title":"Subclasses of univalent functions","volume":"Volume 1013","author":"Salagean","year":"1981","journal-title":"Complex Analysis\u2014Fifth Romanian-Finnish Seminar, Part 1"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Miller, S.S., and Mocanu, P.T. (2000). Differential Subordinations: Theory and Applications, CRC Press.","DOI":"10.1201\/9781482289817"}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/11\/11\/655\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:21:21Z","timestamp":1760145681000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/11\/11\/655"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,11,18]]},"references-count":13,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2022,11]]}},"alternative-id":["axioms11110655"],"URL":"https:\/\/doi.org\/10.3390\/axioms11110655","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2022,11,18]]}}}