Kneser-Type Oscillation Criteria for Half-Linear Third-Order Dynamic Equations on Time Scales

Hassan, Taher S.; Mesmouli, Mouataz Billah; Iambor, Loredana Florentina; Glalah, Belal A.

doi:10.3390/math14111966

Open AccessArticle

Kneser-Type Oscillation Criteria for Half-Linear Third-Order Dynamic Equations on Time Scales

by

Taher S. Hassan

^1,2,3,*

,

Mouataz Billah Mesmouli

¹,

Loredana Florentina Iambor

^4,*

and

Belal A. Glalah

⁵

¹

Department of Mathematics, College of Science, University of Ha’il, Ha’il 2440, Saudi Arabia

²

Jadara University Research Center, Jadara University, Irbid 21110, Jordan

³

Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt

⁴

Department of Mathematics and Computer Science, University of Oradea, Univeritatii nr.1, 410087 Oradea, Romania

⁵

Department of Basic Sciences, Higher Technological Institute 6th of October, 6th of October City 12573, Egypt

^*

Authors to whom correspondence should be addressed.

Mathematics 2026, 14(11), 1966; https://doi.org/10.3390/math14111966

Submission received: 5 April 2026 / Revised: 16 May 2026 / Accepted: 28 May 2026 / Published: 3 June 2026

(This article belongs to the Special Issue Recent Investigations of Differential and Fractional Equations and Inclusions, 3rd Edition)

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Abstract

This paper establishes new Kneser-type oscillation criteria for a class of third-order half-linear dynamic equations on time scales. The analysis is based on a Riccati-type transformation, which reduces the original equation to an associated dynamic inequality and yields explicit oscillation conditions. The obtained criteria extend existing results from second-order to third-order equations and provide a unified treatment of continuous and discrete cases. To the best of our knowledge, no comparable Kneser-type oscillation criteria have been reported for equations of the form considered here. Several examples illustrate the applicability of the main results.

Keywords: Kneser-type; oscillation criteria; third order; dynamic equations; time scales

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MDPI and ACS Style

Hassan, T.S.; Mesmouli, M.B.; Iambor, L.F.; Glalah, B.A. Kneser-Type Oscillation Criteria for Half-Linear Third-Order Dynamic Equations on Time Scales. Mathematics 2026, 14, 1966. https://doi.org/10.3390/math14111966

AMA Style

Hassan TS, Mesmouli MB, Iambor LF, Glalah BA. Kneser-Type Oscillation Criteria for Half-Linear Third-Order Dynamic Equations on Time Scales. Mathematics. 2026; 14(11):1966. https://doi.org/10.3390/math14111966

Chicago/Turabian Style

Hassan, Taher S., Mouataz Billah Mesmouli, Loredana Florentina Iambor, and Belal A. Glalah. 2026. "Kneser-Type Oscillation Criteria for Half-Linear Third-Order Dynamic Equations on Time Scales" Mathematics 14, no. 11: 1966. https://doi.org/10.3390/math14111966

APA Style

Hassan, T. S., Mesmouli, M. B., Iambor, L. F., & Glalah, B. A. (2026). Kneser-Type Oscillation Criteria for Half-Linear Third-Order Dynamic Equations on Time Scales. Mathematics, 14(11), 1966. https://doi.org/10.3390/math14111966

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

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Kneser-Type Oscillation Criteria for Half-Linear Third-Order Dynamic Equations on Time Scales

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