Oscillation for neutral differential equations of canonical form of even-order

Ali Algarni; Ali Algarni

doi:10.3934/math.2025744

AIMS Mathematics

2025, Volume 10, Issue 7: 16611-16623. doi: 10.3934/math.2025744

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Oscillation for neutral differential equations of canonical form of even-order

Ali Algarni ^,

Department of Statistics, Faculty of Science, King AbdulAziz University, P.O. Box 80203, Jeddah, Saudi Arabia

Received: 30 January 2025 Revised: 18 June 2025 Accepted: 24 June 2025 Published: 24 July 2025
MSC : 34C10, 34K11

In this article, I aimed to investigate the oscillatory properties of a novel class of neutral differential equations in their canonical form. I established new relationships between the solutions of the studied equation and their higher-order derivatives to reinforce the monotonic properties of these solutions. Using an iterative process, I present novel and sophisticated oscillatory criteria that broaden the breadth of previous findings in the literature. Several examples are provided to support and elucidate our findings, thereby emphasizing the applicability and significance of the proposed criteria.
- oscillatory,
- even order,
- neutral differential equations
Citation: Ali Algarni. Oscillation for neutral differential equations of canonical form of even-order[J]. AIMS Mathematics, 2025, 10(7): 16611-16623. doi: 10.3934/math.2025744

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Abstract

In this article, I aimed to investigate the oscillatory properties of a novel class of neutral differential equations in their canonical form. I established new relationships between the solutions of the studied equation and their higher-order derivatives to reinforce the monotonic properties of these solutions. Using an iterative process, I present novel and sophisticated oscillatory criteria that broaden the breadth of previous findings in the literature. Several examples are provided to support and elucidate our findings, thereby emphasizing the applicability and significance of the proposed criteria.

References

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