{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:53:44Z","timestamp":1760151224495,"version":"build-2065373602"},"reference-count":17,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2022,3,4]],"date-time":"2022-03-04T00:00:00Z","timestamp":1646352000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100009391","name":"University of Tabuk","doi-asserted-by":"publisher","award":["RGP-0147-1442"],"award-info":[{"award-number":["RGP-0147-1442"]}],"id":[{"id":"10.13039\/100009391","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In recent years, (p,q)-special polynomials, such as p,q-Euler, p,q-Genocchi, p,q-Bernoulli, and p,q-Frobenius-Euler, have been studied and investigated by many mathematicians, as well physicists. It is important that any polynomial have explicit formulas, symmetric identities, summation formulas, and relations with other polynomials. In this work, the (p,q)-sine and (p,q)-cosine Fubini polynomials are introduced and multifarious abovementioned properties for these polynomials are derived by utilizing some series manipulation methods. p,q-derivative operator rules and p,q-integral representations for the (p,q)-sine and (p,q)-cosine Fubini polynomials are also given. Moreover, several correlations related to both the (p,q)-Bernoulli, Euler, and Genocchi polynomials and the (p,q)-Stirling numbers of the second kind are developed.<\/jats:p>","DOI":"10.3390\/sym14030527","type":"journal-article","created":{"date-parts":[[2022,3,6]],"date-time":"2022-03-06T20:40:02Z","timestamp":1646599202000},"page":"527","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["On (p, q)-Sine and (p, q)-Cosine Fubini Polynomials"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4681-9885","authenticated-orcid":false,"given":"Waseem Ahmad","family":"Khan","sequence":"first","affiliation":[{"name":"Department of Mathematics and Natural Sciences, Prince Mohammad Bin Fahd University, P.O. Box 1664, Al Khobar 31952, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5596-5841","authenticated-orcid":false,"given":"Ghulam","family":"Muhiuddin","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5717-1199","authenticated-orcid":false,"given":"Ugur","family":"Duran","sequence":"additional","affiliation":[{"name":"Department of the Basic Concepts of Engineering, Faculty of Engineering and Natural Sciences, Iskenderun Technical University, Hatay 31200, Turkey"}]},{"given":"Deena","family":"Al-Kadi","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2022,3,4]]},"reference":[{"key":"ref_1","first-page":"A29","article-title":"On (p, q)-binomial coefficients","volume":"8","author":"Corcino","year":"2008","journal-title":"Electron. J. Combin. Number Theory"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"555","DOI":"10.5937\/KgJMath1804555D","article-title":"Apostol type (p, q)-Frobenious-Euler polynomials and numbers","volume":"42","author":"Duran","year":"2018","journal-title":"Kragujevac J. Math."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"7833","DOI":"10.1166\/jctn.2016.5785","article-title":"On (p, q)-Bernoulli, (p, q)-Euler and (p, q)-Genocchi polynomials","volume":"13","author":"Duran","year":"2016","journal-title":"J. Comput. Theor. 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Symbolic Comput."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/3\/527\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:32:00Z","timestamp":1760135520000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/3\/527"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,3,4]]},"references-count":17,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2022,3]]}},"alternative-id":["sym14030527"],"URL":"https:\/\/doi.org\/10.3390\/sym14030527","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2022,3,4]]}}}