{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:37:59Z","timestamp":1760146679339,"version":"build-2065373602"},"reference-count":53,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2024,12,2]],"date-time":"2024-12-02T00:00:00Z","timestamp":1733097600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Graduate Studies and Scientific Research at University of Bisha","award":["PNURSP2024R157"],"award-info":[{"award-number":["PNURSP2024R157"]}]},{"DOI":"10.13039\/501100004242","name":"Princess Nourah bint Abdulrahman University","doi-asserted-by":"publisher","award":["PNURSP2024R157"],"award-info":[{"award-number":["PNURSP2024R157"]}],"id":[{"id":"10.13039\/501100004242","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The goal of this study is to derive new conditions that improve the testing of the oscillatory and asymptotic features of fourth-order differential equations with an advanced neutral term. By using Riccati techniques and comparison with lower-order equations, we establish new criteria that verify the absence of positive solutions and, consequently, the oscillation of all solutions to the investigated equation. Using our results to analyze a few specific instances of the examined equation, we can ultimately clarify the significance of the new inequalities. Our results are an extension of previous results that considered equations with a neutral delay term and also an improvement of previous results that considered only equations with an advanced neutral term.<\/jats:p>","DOI":"10.3390\/axioms13120847","type":"journal-article","created":{"date-parts":[[2024,12,4]],"date-time":"2024-12-04T10:07:10Z","timestamp":1733306830000},"page":"847","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Functional Differential Equations with an Advanced Neutral Term: New Monotonic Properties of Recursive Nature to Optimize Oscillation Criteria"],"prefix":"10.3390","volume":"13","author":[{"given":"Amany","family":"Nabih","sequence":"first","affiliation":[{"name":"Department of Basic Sciences, Higher Future Institute of Engineering and Technology, Mansoura 35111, Egypt"}]},{"given":"Wedad","family":"Albalawi","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia"}]},{"given":"Mohammad S.","family":"Jazmati","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, Qassim University, P.O. Box 6644, Buraydah 51452, Saudi Arabia"}]},{"given":"Ali","family":"Elrashidi","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, College of Engineering, University of Business and Technology, Jeddah 21448, Saudi Arabia"},{"name":"Engineering Mathematics Department, Faculty of Engineering, Alexandria University, Alexandria 11865, Egypt"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0159-6726","authenticated-orcid":false,"given":"Hegagi M.","family":"Ali","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, University of Bisha, Bisha 61922, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3850-1022","authenticated-orcid":false,"given":"Osama","family":"Moaaz","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, Qassim University, P.O. Box 6644, Buraydah 51452, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2024,12,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Braun, M., and Golubitsky, M. (1983). Differential Equations and Their Applications, Springer.","DOI":"10.1007\/978-1-4684-0164-6"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Hale, J.K. (1971). Functional differential equations. Analytic Theory of Differential Equations, Springer.","DOI":"10.1007\/978-1-4615-9968-5"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Courant, R., and Hilbert, D. (1989). Methods of Mathematical Physics, Wiley Classics Library.","DOI":"10.1002\/9783527617210"},{"key":"ref_4","unstructured":"Zhang, Z. (1992). Qualitative Theory of Differential Equations, American Mathematical Society."},{"key":"ref_5","unstructured":"Nemytskii, V.V. (2015). Qualitative Theory of Differential Equations. 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