Iterative oscillation criteria of third-order nonlinear damped neutral differential equations

Taher S. Hassan; Emad R. Attia; Bassant M. El-Matary; Taher S. Hassan; Emad R. Attia; Bassant M. El-Matary

doi:10.3934/math.20241124

AIMS Mathematics

2024, Volume 9, Issue 8: 23128-23141. doi: 10.3934/math.20241124

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Research article

Iterative oscillation criteria of third-order nonlinear damped neutral differential equations

1.
Department of Mathematics, College of Science, University of Hail, Hail 2440, Saudi Arabia
2.
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
3.
Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele Ⅱ, 39, 00186 Roma, Italy
4.
Department of Mathematics, College of Sciences and Humanities, Prince Sattam Bin Abdulaziz University, Alkharj 11942, Saudi Arabia
5.
Department of Mathematics, Faculty of Science, Damietta University, New Damietta 34517, Egypt
6.
Department of Mathematics, College of Science, Qassim University, Buraydah, 51452, Saudi Arabia

Received: 07 May 2024 Revised: 09 July 2024 Accepted: 22 July 2024 Published: 29 July 2024
MSC : 34K11, 39A10, 39A99

Using comparison principles, we examine the asymptotic characteristics of a third-order nonlinear damped neutral differential equation. Our results substantially generalize numerous previously established results as well as drastically improving them. To illustrate the relevance and effectiveness of our results, we use numerical examples.
- differential equations,
- third-order,
- oscillation,
- asymptotic behavior,
- damped
Citation: Taher S. Hassan, Emad R. Attia, Bassant M. El-Matary. Iterative oscillation criteria of third-order nonlinear damped neutral differential equations[J]. AIMS Mathematics, 2024, 9(8): 23128-23141. doi: 10.3934/math.20241124

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Abstract

Using comparison principles, we examine the asymptotic characteristics of a third-order nonlinear damped neutral differential equation. Our results substantially generalize numerous previously established results as well as drastically improving them. To illustrate the relevance and effectiveness of our results, we use numerical examples.

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