{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,11]],"date-time":"2026-06-11T15:03:37Z","timestamp":1781190217485,"version":"3.54.1"},"reference-count":35,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,3,14]],"date-time":"2025-03-14T00:00:00Z","timestamp":1741910400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Graduate Studies and Scientific Research at Jouf University","award":["DGSSR-2024-02-02070"],"award-info":[{"award-number":["DGSSR-2024-02-02070"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, we define a new generalization of three-variable q-Laguerre polynomials and derive some properties. By using these polynomials, we introduce a new generalization of three-variable q-Laguerre-based Appell polynomials (3VqLbAP) through a generating function approach involving zeroth-order q-Bessel\u2013Tricomi functions. These polynomials are studied by means of generating function, series expansion, and determinant representation. Also, these polynomials are further examined within the framework of q-quasi-monomiality, leading to the establishment of essential operational identities. We then derive operational representations, as well as q-differential equations for the three-variable q-Laguerre-based Appell polynomials. Some examples are constructed in terms of q-Laguerre\u2013Hermite-based Bernoulli, Euler, and Genocchi polynomials in order to illustrate the main results.<\/jats:p>","DOI":"10.3390\/sym17030439","type":"journal-article","created":{"date-parts":[[2025,3,14]],"date-time":"2025-03-14T13:07:51Z","timestamp":1741957671000},"page":"439","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["A New Generalization of q-Laguerre-Based Appell Polynomials and Quasi-Monomiality"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1679-8358","authenticated-orcid":false,"given":"Naeem","family":"Ahmad","sequence":"first","affiliation":[{"name":"Mathematics Department, College of Science, Jouf University, Sakaka 72388, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4681-9885","authenticated-orcid":false,"given":"Waseem Ahmad","family":"Khan","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Prince Mohammad Bin Fahd University, P.O. Box 1664, Al Khobar 31952, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,3,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1016\/S0377-0427(99)00111-9","article-title":"Generalized polynomials and associated operational identities","volume":"108","author":"Dattoli","year":"1999","journal-title":"J. Comput. Appl. Math."},{"key":"ref_2","first-page":"329","article-title":"q-Bessel functions: The point of view of the generating function method","volume":"17","author":"Dattoli","year":"1997","journal-title":"Rend. Mat. Appl."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1016\/S0969-806X(99)00346-1","article-title":"Exponential operators, quasi-monomials and generalized polynomials","volume":"57","author":"Dattoli","year":"2000","journal-title":"Radiat. Phys. Chem."},{"key":"ref_4","first-page":"223","article-title":"On a new family of Laguerre polynomials","volume":"134","author":"Dattoli","year":"2000","journal-title":"Atti Accad. Sci. Torino Cl. Sci. Fis. Mat. Nat."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1006\/aphy.1993.1003","article-title":"Quantum algebras and q-special functions","volume":"221","author":"Florenini","year":"1993","journal-title":"Ann. Phys."},{"key":"ref_6","first-page":"64","article-title":"On q-functions and a certain difference operator","volume":"46","author":"Jackson","year":"1908","journal-title":"Trans. R. Soc. Edinb."},{"key":"ref_7","first-page":"193","article-title":"On q-definite integral","volume":"41","author":"Jackson","year":"1910","journal-title":"Q. J. Pure Appl. Math."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Sheng, Y., and Zhang, T. (2022). Results on the q-calculus and fractional q-differential equations. Mathematics, 10.","DOI":"10.3390\/math10010064"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"106282","DOI":"10.1016\/j.aml.2020.106282","article-title":"The solution theory of the nonlinear q-fractional differential equations","volume":"104","author":"Zhang","year":"2020","journal-title":"Appl. Math. Lett."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2050121","DOI":"10.1142\/S0218348X20501212","article-title":"A difference method for solving the nonlinear q-fractional differential equations on time scales","volume":"28","author":"Zhang","year":"2020","journal-title":"Fractals"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"341","DOI":"10.2991\/jnmp.2007.14.3.4","article-title":"Fractional q-calculus on a time scales","volume":"14","author":"Atici","year":"2007","journal-title":"J. Nonlinear Math. Phys."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Yang, X.-J. (2021). Theory and Applications of Special Functions for Scientists and Engineers, Springer Nature.","DOI":"10.1007\/978-981-33-6334-2"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Yang, X.-J., Baleanu, D., and Srivastava, H.M. (2016). Local Fractional Integral Transforms and Their Applications, Elsevier.","DOI":"10.1016\/B978-0-12-804002-7.00002-4"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Abdeljawad, T., and Benil, B. (2012). A quantum generalized Mittag-Leffler function via Caputo fractional linear equations. Abstract and Applied Analysis, Hindawi Publishing Corporation.","DOI":"10.1155\/2012\/546062"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Andrews, G.E., Askey, R., and Roy, R. (1999). Special Functions, Cambridge University Press.","DOI":"10.1017\/CBO9781107325937"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1016\/0021-9045(86)90062-6","article-title":"Limits of some q-Laguerre polynomials","volume":"46","author":"Askey","year":"1986","journal-title":"J. Approx. Theory"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Alatawi, M.S., Khan, W.A., and Ryoo, C.S. (2022). Explicit properties of q-Cosine and q-Sine Array-type polynomials containing symmetric structures. Symmetry, 14.","DOI":"10.3390\/sym14081675"},{"key":"ref_18","first-page":"759","article-title":"A new class of q-Hermite based Apostol type Frobenius Genocchi polynomials","volume":"35","author":"Kang","year":"2020","journal-title":"Commun. Korean Math. Soc."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"26799","DOI":"10.3934\/math.20241303","article-title":"Advancements in q-Hermite-Appell polynomials: A three-dimensional exploration","volume":"9","author":"Zayed","year":"2024","journal-title":"AIMS Math."},{"key":"ref_20","first-page":"153","article-title":"Symmetric q-Bessel functions","volume":"51","author":"Dattoli","year":"1996","journal-title":"Matematiche"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"128126","DOI":"10.1016\/j.jmaa.2024.128126","article-title":"Two-variable q-Laguerre polynomials from the context of quasi-monomiality","volume":"535","author":"Cao","year":"2024","journal-title":"J. Anal. Appl."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2412545","DOI":"10.1080\/27690911.2024.2412545","article-title":"Bivariate q-Laguerre-Appell polynomials and their applications","volume":"32","author":"Fadel","year":"2024","journal-title":"Appl. Math. Sci. Eng."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"8705","DOI":"10.3934\/math.2021506","article-title":"On 2-variable q-Hermite polynomials","volume":"6","author":"Raza","year":"2021","journal-title":"AIMS Math."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1002\/mana.19580170311","article-title":"q-Bernoulli numbers and polynomials","volume":"17","year":"1958","journal-title":"Math. Nachr."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1007\/BF02416939","article-title":"q-Appell polynomials","volume":"77","year":"1967","journal-title":"Ann. Mat. Pura Appl."},{"key":"ref_26","first-page":"147","article-title":"Hermite-Bessel and Laguerre-Bessel functions: A by-product of the monomiality principle","volume":"1","author":"Dattoli","year":"2020","journal-title":"Adv. Spec. Funct. Appl."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Fadel, M., Alatawi, M.S., and Khan, W.A. (2024). Two variable q-Hermite-based Appell polynomials and their applications. Mathematics, 12.","DOI":"10.3390\/math12091358"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1007\/BF02392231","article-title":"The poweroid, an extension of the mathematical notion of power","volume":"73","author":"Steffensen","year":"1941","journal-title":"Acta Math."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Alam, N., Khan, W.A., Kizilates, C., and Ryoo, C.S. (2025). Two variable q-General-Appell polynomials within the context of the monomiality principle. Mathematics, 13.","DOI":"10.3390\/math13050765"},{"key":"ref_30","first-page":"328032","article-title":"General Appell polynomials within the context of monomiality principle","volume":"2013","author":"Khan","year":"2013","journal-title":"Int. J. Anal."},{"key":"ref_31","first-page":"351","article-title":"A study on q-Appell polynomials from determinantal point of view","volume":"260","author":"Kelestheri","year":"2015","journal-title":"Appl. Math. Comput."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Costabile, F.A., Gualtieri, M.T., and Napoli, A. (2021). General bivariate Appell polynomials via matrix calculus and related interpolation hints. Mathematics, 9.","DOI":"10.3390\/math9090964"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"531","DOI":"10.1007\/s11075-022-01272-4","article-title":"Bivariate general Appell interpolation problem","volume":"91","author":"Costabile","year":"2022","journal-title":"Numer. Algorithms"},{"key":"ref_34","first-page":"31","article-title":"q-Bernoulli and q-Euler polynomials, an umbral calculus approach","volume":"1","author":"Ernst","year":"2006","journal-title":"Int. J. Differ. Equ."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Ernst, T. (2012). A Comprehensive Treatment of q-Calculus, Springer.","DOI":"10.1007\/978-3-0348-0431-8"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/3\/439\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T16:54:06Z","timestamp":1760028846000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/3\/439"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,3,14]]},"references-count":35,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2025,3]]}},"alternative-id":["sym17030439"],"URL":"https:\/\/doi.org\/10.3390\/sym17030439","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,3,14]]}}}