{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:15:42Z","timestamp":1760148942122,"version":"build-2065373602"},"reference-count":73,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2023,6,16]],"date-time":"2023-06-16T00:00:00Z","timestamp":1686873600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Arab Open University","award":["AOURG-2023-007"],"award-info":[{"award-number":["AOURG-2023-007"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Using the concepts of q-fractional calculus operator theory, we first define a (\u03bb,q)-differintegral operator, and we then use m-fold symmetric functions to discover a new family of bi-close-to-convex functions. First, we estimate the general Taylor\u2013Maclaurin coefficient bounds for a newly established class using the Faber polynomial expansion method. In addition, the Faber polynomial method is used to examine the Fekete\u2013Szeg\u00f6 problem and the unpredictable behavior of the initial coefficient bounds of the functions that belong to the newly established class of m-fold symmetric bi-close-to-convex functions. Our key results are both novel and consistent with prior research, so we highlight a few of their important corollaries for a comparison.<\/jats:p>","DOI":"10.3390\/axioms12060600","type":"journal-article","created":{"date-parts":[[2023,6,16]],"date-time":"2023-06-16T10:19:22Z","timestamp":1686910762000},"page":"600","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["New Applications of Faber Polynomials and q-Fractional Calculus for a New Subclass of m-Fold Symmetric bi-Close-to-Convex Functions"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5053-5028","authenticated-orcid":false,"given":"Mohammad Faisal","family":"Khan","sequence":"first","affiliation":[{"name":"Department of Basic Sciences, College of Science and Theoretical Studies, Saudi Electronic University, Riyadh 11673, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9960-2591","authenticated-orcid":false,"given":"Suha B.","family":"Al-Shaikh","sequence":"additional","affiliation":[{"name":"Faculty of Computer Studies, Arab Open University, Riyadh 11681, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0694-1680","authenticated-orcid":false,"given":"Ahmad A.","family":"Abubaker","sequence":"additional","affiliation":[{"name":"Faculty of Computer Studies, Arab Open University, Riyadh 11681, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Khaled","family":"Matarneh","sequence":"additional","affiliation":[{"name":"Faculty of Computer Studies, Arab Open University, Riyadh 11681, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,6,16]]},"reference":[{"key":"ref_1","first-page":"1","article-title":"Uber Uber die Konforme Abbildung Sterngebieten","volume":"63","author":"Nevalinna","year":"1920","journal-title":"Oversiktav-Fin. 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