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Research Article | Open Access

Enhanced Kneser-type oscillation criteria for second-order functional quasilinear dynamic equations on time scales

Taher S. Hassan1,2,3, Elvan Akın4, Bassant M. El-Matary5( ), Ioan-Lucian Popa6,7( ), Mouataz Billah Mesmouli1, Ismoil Odinaev8, Akbar Ali1
Department of Mathematics, College of Science, University of Ha'il, Ha'il, 2440, Saudi Arabia
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, 35516, Egypt
Jadara University Research Center, Jadara University, Irbid 21110, Jordan
Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO 65401, USA
Department of Mathematics, College of Science, Qassim University, Buraydah, 51452, Saudi Arabia
Department of Computing, Mathematics and Electronics, 1 Decembrie 1918 University of Alba Iulia, 510009 Alba Iulia, Romania
Faculty of Mathematics and Computer Science, Transilvania University of Brasov, Iuliu Maniu Street 50, 500091 Brasov, Romania
Department of Automated Electrical Systems, Ural Power Engineering Institute, Ural Federal University, 620002 Yekaterinburg, Russia
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Abstract

This work presents new Kneser-type oscillation criteria for second-order quasilinear functional dynamic equations defined on arbitrary unbounded above time scales. Our approach employs the Riccati transformation technique in conjunction with the integral averaging method. The results show a significant improvement over recent Kneser-type oscillation criteria. We provided several illustrative examples to highlight the importance of our findings.

Keywords

oscillationKneser-typequasilineardifferential equationsdynamic equationstime scales
CLC number: 26E70, 34C10, 34K11, 34K42, 34N05

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AIMS Mathematics
Volume 10 Issue 10,
October 2025
Pages 23789-23802
DOI: 10.3934/math.20251057

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Cite this article:
Hassan TS, Akın E, El-Matary BM, et al. Enhanced Kneser-type oscillation criteria for second-order functional quasilinear dynamic equations on time scales. AIMS Mathematics, 2025, 10(10): 23789-23802. https://doi.org/10.3934/math.20251057

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Received: 20 February 2025
Revised: 22 July 2025
Accepted: 30 July 2025
Published: 20 October 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)