{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T00:38:47Z","timestamp":1759970327953,"version":"build-2065373602"},"reference-count":34,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2025,1,13]],"date-time":"2025-01-13T00:00:00Z","timestamp":1736726400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002383","name":"King Saud University, Riyadh, Saudi Arabia","doi-asserted-by":"publisher","award":["RSPD2024R533"],"award-info":[{"award-number":["RSPD2024R533"]}],"id":[{"id":"10.13039\/501100002383","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This study presents novel and generalizable sufficient conditions for determining the oscillatory behavior of solutions to higher-order half-linear neutral delay dynamic equations on time scales. Utilizing the Riccati transformation technique in combination with Taylor monomials, we derive new and comprehensive oscillation criteria that cover a wide range of cases, including super-linear, half-linear, and sublinear equations. These results extend and improve upon existing oscillation criteria found in the literature by introducing more general conditions and providing a broader applicability to different types of dynamic equations. Furthermore, the study highlights the role of symmetry in the underlying equations, demonstrating how symmetry properties can be leveraged to simplify the analysis and provide additional insights into oscillatory behavior. To demonstrate the practical relevance of our findings, we include illustrative examples that show how these new criteria, along with symmetry-based perspectives, can be effectively applied to various time scales.<\/jats:p>","DOI":"10.3390\/sym17010116","type":"journal-article","created":{"date-parts":[[2025,1,13]],"date-time":"2025-01-13T09:49:17Z","timestamp":1736761757000},"page":"116","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Investigating Oscillations in Higher-Order Half-Linear Dynamic Equations on Time Scales"],"prefix":"10.3390","volume":"17","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\/0000-0002-1167-2430","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"}]},{"given":"Monica","family":"Botros","sequence":"additional","affiliation":[{"name":"Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy"},{"name":"Basic Science Department, Faculty of Engineering, Delta University for Science and Technology, Gamasa 11152, Egypt"}]}],"member":"1968","published-online":{"date-parts":[[2025,1,13]]},"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":"Agarwal, R. (2000). 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