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Research Article | Open Access

Improved Kneser-type oscillation criterion for half-linear dynamic equations on time scales

Taher S. Hassan1( ), Amir Abdel Menaem2,3, Hasan Nihal Zaidi1, Khalid Alenzi1, Bassant M. El-Matary4( )
Department of Mathematics, College of Science, University of Ha'il, Ha'il 2440, Saudi Arabia
Department of Automated Electrical Systems, Ural Power Engineering Institute, Ural Federal University, 620002 Yekaterinburg, Russia
Electrical Engineering Department, Mansoura University, Mansoura 35516, Egypt
Department of Mathematics, College of Science, Qassim University, Buraydah, 51452, Saudi Arabia
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Abstract

We study the Kneser-type oscillation criterion for a class of second-order half-linear functional dynamic equations on an arbitrary time scale utilizing the integral averaging approach and the Riccati transformation method. The results show an improvement in Kneser-type when compared to some known results. We provide some illustrative examples to demonstrate the significance of our main results.

Keywords

oscillation criteriaKneser-typehalf-lineardynamic equationtime scalesdifferential equations
CLC number: 39A10, 39A21, 39A99, 34C10, 34C15, 34K11, 34K42, 34N05

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AIMS Mathematics
Volume 9 Issue 10,
October 2024
Pages 29425-29438
DOI: 10.3934/math.20241426

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Cite this article:
Hassan TS, Menaem AA, Zaidi HN, et al. Improved Kneser-type oscillation criterion for half-linear dynamic equations on time scales. AIMS Mathematics, 2024, 9(10): 29425-29438. https://doi.org/10.3934/math.20241426

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Received: 31 August 2024
Revised: 29 September 2024
Accepted: 08 October 2024
Published: 15 October 2024
©2024 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)