{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,8]],"date-time":"2026-05-08T12:16:47Z","timestamp":1778242607811,"version":"3.51.4"},"reference-count":33,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2024,1,23]],"date-time":"2024-01-23T00:00:00Z","timestamp":1705968000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100005911","name":"Najran University","doi-asserted-by":"publisher","award":["NU\/DRP\/SERC\/12\/4"],"award-info":[{"award-number":["NU\/DRP\/SERC\/12\/4"]}],"id":[{"id":"10.13039\/501100005911","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, we introduce a new class of special polynomials called the generalized Bell polynomials, constructed by combining two-variable general polynomials with two-variable Bell polynomials. The concept of the monomiality principle was employed to establish the generating function and obtain various results for these polynomials. We explore certain related identities, properties, as well as differential and integral formulas. Further, specific members within the generalized Bell family\u2014such as the Gould-Hopper-Bell polynomials, Laguerre-Bell polynomials, truncated-exponential-Bell polynomials, Hermite-Appell-Bell polynomials, and Fubini-Bell polynomials\u2014were examined, unveiling analogous outcomes for each. Finally, Mathematica was utilized to investigate the zero distributions of the Gould-Hopper-Bell polynomials.<\/jats:p>","DOI":"10.3390\/axioms13020073","type":"journal-article","created":{"date-parts":[[2024,1,23]],"date-time":"2024-01-23T07:22:32Z","timestamp":1705994552000},"page":"73","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["On Generalized Class of Bell Polynomials Associated with Geometric Applications"],"prefix":"10.3390","volume":"13","author":[{"given":"Rashad A.","family":"Al-Jawfi","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Sciences and Arts, Najran University, Najran 55461, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7979-8064","authenticated-orcid":false,"given":"Abdulghani","family":"Muhyi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Hajjah University, Hajjah, Yemen"},{"name":"Department of Mechatronics Engineering, Faculty of Engineering and Smart Computing, Modern Specialized University, Sana\u2019a, Yemen"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8862-0623","authenticated-orcid":false,"given":"Wadia Faid Hassan","family":"Al-shameri","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Sciences and Arts, Najran University, Najran 55461, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,1,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"258","DOI":"10.2307\/1968431","article-title":"Exponential polynomials","volume":"35","author":"Bell","year":"1934","journal-title":"Ann. 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