{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T00:43:19Z","timestamp":1759970599328,"version":"build-2065373602"},"reference-count":22,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2025,1,26]],"date-time":"2025-01-26T00:00:00Z","timestamp":1737849600000},"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 paper, without assuming any extra conditions, the third-order unstable noncaonical advanced differential equation is changed into a canonical form that reduces the number of classes of nonoscillatory solutions into two instead of four. Using comparison and integral averaging method, new sufficient conditions are obtained so that all solutions to have Property B or oscillate. Specific numerical examples are provided to demonstrate the importance and the significance of the main results.<\/jats:p>","DOI":"10.3390\/axioms14020091","type":"journal-article","created":{"date-parts":[[2025,1,28]],"date-time":"2025-01-28T08:57:48Z","timestamp":1738054668000},"page":"91","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Noncanonical Third-Order Advanced Differential Equations of Unstable Type: Oscillation and Property B via Canonical Transform"],"prefix":"10.3390","volume":"14","author":[{"given":"Bose","family":"Rani","sequence":"first","affiliation":[{"name":"Department of Mathematics, Sri Kanyaka Parameswari Arts and Science College for Women, Chennai 600103, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0477-1895","authenticated-orcid":false,"given":"George E.","family":"Chatzarakis","sequence":"additional","affiliation":[{"name":"Department of Electrical and Electronic Engineering Educators, School of Pedagogical and Technological Education, 15122 Marousi, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ethiraju","family":"Thandapani","sequence":"additional","affiliation":[{"name":"Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai 600005, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,1,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Gyori, I., and Ladas, G. 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Math."},{"key":"ref_9","first-page":"265","article-title":"Oscillation of noncanonical third-order delay differential equations via canonical transform","volume":"23","author":"Srinivasan","year":"2023","journal-title":"Appl. Math. E-Notes"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1341","DOI":"10.1515\/ms-2017-0312","article-title":"Asymptotic properties of noncanonical third-order differential equations","volume":"69","author":"Baculikova","year":"2019","journal-title":"Math. Slovaca"},{"key":"ref_11","first-page":"128950","article-title":"Remarks on the oscillation of nonlinear third-order noncanonical delay differential equations","volume":"481","author":"Prabaharan","year":"2024","journal-title":"Appl. Math. Comput."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Kiguradze, I.T., and Chanturia, T.A. (1993). 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Appl."},{"key":"ref_18","first-page":"102","article-title":"On the oscillation of certain third-order nonlinear functional differential equations","volume":"202","author":"Grace","year":"2008","journal-title":"Appl. Math. Comput."},{"key":"ref_19","first-page":"55","article-title":"Oscillation of half-linear differential equation with mixed type of arguments","volume":"10","author":"Dzurina","year":"2013","journal-title":"Electron. J. Qual. Theory Differ. Equ."},{"key":"ref_20","first-page":"1","article-title":"Property (B) and oscillation of third-order differential equation with mixed type of arguments","volume":"19","author":"Dzurina","year":"2022","journal-title":"J. Appl. Anal."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"180","DOI":"10.1007\/s00009-023-02342-0","article-title":"New criteria on oscillatory behavior of third-order half-linear functional differential equations","volume":"20","author":"Grace","year":"2023","journal-title":"Mediterr. J. Math."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1090\/S0002-9947-1974-0330632-X","article-title":"Canonical forms and principal systems for general disconjugate equations","volume":"189","author":"Trench","year":"1974","journal-title":"Trans. Am. Math. 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