{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T11:58:27Z","timestamp":1776772707260,"version":"3.51.2"},"reference-count":45,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2025,9,18]],"date-time":"2025-09-18T00:00:00Z","timestamp":1758153600000},"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>This paper explores the eigenfunctions of specific Laguerre-type parametric operators to develop multi-parametric models, which are associated with a class of the generalized Mittag-Leffler type functions, for dynamical systems and population dynamics. By leveraging these multi-parametric approaches, we introduce new concepts in number theory, specifically those involving multi-parametric Bernoulli and Euler numbers, along with other related polynomials. Several numerical examples, which are generated by using the computer algebra program Mathematica\u00a9 (Version 14.3), demonstrate the effectiveness of the models that we have presented and analyzed in this paper.<\/jats:p>","DOI":"10.3390\/axioms14090705","type":"journal-article","created":{"date-parts":[[2025,9,19]],"date-time":"2025-09-19T08:11:01Z","timestamp":1758269461000},"page":"705","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A Note on Multi-Index Mittag-Leffler Functions and Parametric Laguerre-Type Exponentials"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9277-8092","authenticated-orcid":false,"given":"Hari Mohan","family":"Srivastava","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada"},{"name":"Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan"},{"name":"Center for Converging Humanities, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul 02447, Republic of Korea"},{"name":"Department of Applied Mathematics, Chung Yuan Christian University, Chung-Li, Taoyuan City 20314, Taiwan"},{"name":"Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, AZ1007 Baku, Azerbaijan"},{"name":"Mathematics Section, International Telematic University UniNettuno, 39 Corso Vittorio Emanuele II, I-00186 Rome, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0969-884X","authenticated-orcid":false,"given":"Diego","family":"Caratelli","sequence":"additional","affiliation":[{"name":"Department of Research and Development, The Antenna Company, 5656 AE Eindhoven, The Netherlands"},{"name":"Department of Electrical Engineering, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7899-3087","authenticated-orcid":false,"given":"Paolo Emilio","family":"Ricci","sequence":"additional","affiliation":[{"name":"Mathematics Section, International Telematic University UniNettuno, 39 Corso Vittorio Emanuele II, I-00186 Rome, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,9,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"378","DOI":"10.2478\/s13540-013-0024-9","article-title":"Multi-parametric Mittag-Leffler functions and their extension","volume":"16","author":"Kilbas","year":"2013","journal-title":"Fract. 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