{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,21]],"date-time":"2026-02-21T04:07:13Z","timestamp":1771646833466,"version":"3.50.1"},"reference-count":46,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2022,9,12]],"date-time":"2022-09-12T00:00:00Z","timestamp":1662940800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"United Arab Emirates University","award":["UPAR 31S315"],"award-info":[{"award-number":["UPAR 31S315"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Many diverse subclasses of analytic functions, q-starlike functions, and symmetric q-starlike functions have been studied and analyzed by using q-analogous values of integral and derivative operators. In this paper, we define a q-analogous value of differential operators for harmonic functions with the help of basic concepts of quantum (q-) calculus operator theory; and introduce a new subclass of harmonic functions associated with the Janowski and q-Mittag\u2013Leffler functions. We obtain several useful properties of the new class, such as necessary and sufficient conditions, criteria for analyticity, compactness, convexity, extreme points, radii of starlikeness, radii of convexity, distortion bounds, and integral mean inequality. Furthermore, we discuss some applications of this study in the form of some results and examples and highlight some known corollaries for verifying our main results presented in this investigation. Finally, the conclusion section summarizes the fact about the (p,q)-variations.<\/jats:p>","DOI":"10.3390\/sym14091905","type":"journal-article","created":{"date-parts":[[2022,9,13]],"date-time":"2022-09-13T22:37:28Z","timestamp":1663108648000},"page":"1905","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Applications of a q-Differential Operator to a Class of Harmonic Mappings Defined by q-Mittag\u2013Leffler Functions"],"prefix":"10.3390","volume":"14","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\/0000-0001-5287-4656","authenticated-orcid":false,"given":"Isra","family":"Al-shbeil","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, The University of Jordan, Amman 11942, Jordan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0361-4887","authenticated-orcid":false,"given":"Shahid","family":"Khan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Riphah International University, Islamabad 44000, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1123-8578","authenticated-orcid":false,"given":"Nazar","family":"Khan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad 22500, Pakistan"}]},{"given":"Wasim Ul","family":"Haq","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad 22500, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2909-0970","authenticated-orcid":false,"given":"Jianhua","family":"Gong","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, United Arab Emirates University, Al Ain 18006, United Arab Emirates"}]}],"member":"1968","published-online":{"date-parts":[[2022,9,12]]},"reference":[{"key":"ref_1","unstructured":"Ponnusamy, S., and Silverman, H. 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