{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,3]],"date-time":"2026-02-03T03:58:03Z","timestamp":1770091083152,"version":"3.49.0"},"reference-count":25,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2026,2,2]],"date-time":"2026-02-02T00:00:00Z","timestamp":1769990400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this work, we construct a new class of Appell-type polynomials generated through extended truncated and truncated exponential kernels, and we analyze their core algebraic and operational features. In particular, we establish a suitable recurrence scheme and obtain the associated multiplicative and differential operators. By confirming the quasi-monomial structure, we further deduce the governing differential equation for the proposed family. In addition, we present both a series expansion and a determinant formulation, providing complementary representations that are useful for symbolic manipulation and computation. As special cases, we introduce and study subfamilies arising from this setting, namely, extended truncated exponential versions of the Bernoulli, Euler, and Genocchi polynomials, and discuss their structural identities and operational behavior. Overall, these developments broaden the theory of special polynomials and furnish tools relevant to problems in mathematical physics and differential equations.<\/jats:p>","DOI":"10.3390\/axioms15020111","type":"journal-article","created":{"date-parts":[[2026,2,2]],"date-time":"2026-02-02T15:38:12Z","timestamp":1770046692000},"page":"111","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Note on Truncated Exponential-Based Appell Polynomials via Fractional Operators"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4681-9885","authenticated-orcid":false,"given":"Waseem Ahmad","family":"Khan","sequence":"first","affiliation":[{"name":"Department of Electrical Engineering, Prince Mohammad Bin Fahd University, P.O. Box 1664, Al Khobar 31952, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Francesco Aldo","family":"Costabile","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, University of Calabria, 87036 Rende, CS, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8309-6121","authenticated-orcid":false,"given":"Khidir Shaib","family":"Mohamed","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alawia","family":"Adam","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6484-469X","authenticated-orcid":false,"given":"Shahid Ahmad","family":"Wani","sequence":"additional","affiliation":[{"name":"Symbiosis Institute of Technology Pune, Symbiosis International (Deemed) University, Pune 412115, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,2,2]]},"reference":[{"key":"ref_1","first-page":"595","article-title":"A note on truncated polynomials","volume":"134","author":"Dattoli","year":"2003","journal-title":"Appl. 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