{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:34:23Z","timestamp":1760146463093,"version":"build-2065373602"},"reference-count":28,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2024,11,2]],"date-time":"2024-11-02T00:00:00Z","timestamp":1730505600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"King Saud University","award":["RSPD2024R533"],"award-info":[{"award-number":["RSPD2024R533"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This study aims to establish novel iterative oscillation criteria for second-order half-linear advanced dynamic equations in non-canonical form. The results extend and enhance recently established criteria for this type of equation by various authors and also encompass the classical criteria for related ordinary differential equations. Our methodology involves transforming the non-canonical equation into its corresponding canonical form. The inherent symmetry of these canonical forms plays a pivotal role in deriving our new criteria. By employing techniques from the theory of symmetric differential equations and utilizing symmetric functions, we establish precise conditions for oscillation. Several illustrative examples highlight the accuracy, applicability, and versatility of our results.<\/jats:p>","DOI":"10.3390\/sym16111457","type":"journal-article","created":{"date-parts":[[2024,11,4]],"date-time":"2024-11-04T03:57:34Z","timestamp":1730692654000},"page":"1457","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Enhanced Oscillation Criteria for Non-Canonical Second-Order Advanced Dynamic Equations on Time Scales"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4166-9985","authenticated-orcid":false,"given":"Ahmed M.","family":"Hassan","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Benha University, Benha-Kalubia 13518, Egypt"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3850-1022","authenticated-orcid":false,"given":"Osama","family":"Moaaz","sequence":"additional","affiliation":[{"name":"Section of Mathematics, International Telematic University Uninettuno, CorsoVittorio Emanuele II, 39, 00186 Roma, Italy"},{"name":"Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1167-2430","authenticated-orcid":false,"given":"Sameh S.","family":"Askar","sequence":"additional","affiliation":[{"name":"Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7103-8872","authenticated-orcid":false,"given":"Ahmad M.","family":"Alshamrani","sequence":"additional","affiliation":[{"name":"Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9164-798X","authenticated-orcid":false,"given":"Samy E.","family":"Affan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Benha University, Benha-Kalubia 13518, Egypt"}]}],"member":"1968","published-online":{"date-parts":[[2024,11,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1007\/BF03323153","article-title":"Analysis on measure chains\u2014A unified approach to continuous and discrete calculus","volume":"18","author":"Hilger","year":"1990","journal-title":"Results Math."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Bohner, M., and Peterson, A. (2001). Dynamic Equations on Time Scales: An Introduction with Applications, Springer.","DOI":"10.1007\/978-1-4612-0201-1"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Bohner, M., and Peterson, A. (2002). 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