Optimized properties for noncanonical neutral differential equations with distributed deviating arguments and their oscillation analysis

Osama Moaaz; Asma Al-Jaser; Mohamed F. Abouelenein; Mona Anis; Osama Moaaz; Asma Al-Jaser; Mohamed F. Abouelenein; Mona Anis

doi:10.3934/math.2026727

AIMS Mathematics

2026, Volume 11, Issue 6: 17838-17858. doi: 10.3934/math.2026727

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Optimized properties for noncanonical neutral differential equations with distributed deviating arguments and their oscillation analysis

1.
Department of Mathematics, College of Science, Qassim University, P.O. Box 6644, Buraydah 51452, Saudi Arabia
2.
Department of Mathematics, Faculty of Science, Mansoura University, 35516 Mansoura, Egypt
3.
Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
4.
Department of Insurance and Risk Management, College of Business, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Riyadh, Saudi Arabia

Received: 31 March 2026 Revised: 19 May 2026 Accepted: 08 June 2026 Published: 18 June 2026
MSC : 34C10, 34K11

This work develops new oscillation criteria for second‑order neutral differential equations with distributed deviating arguments. The analysis covers both the noncanonical case and the situation in which the coefficient of the neutral delay term exceeds one, settings that remain insufficiently addressed in the existing literature. The main contribution of this study is the derivation of several refined inequalities that strengthen the relation between the solution and its associated function. These improved relations allow us to establish sharper oscillation criteria, including a Kneser ‑type criterion and additional forms that extend and refine earlier approaches. Several examples are provided to apply the theoretical results and to compare them with related findings. The findings indicate that the developed framework offers a more sensitive and robust tool for detecting oscillatory behavior in this class of neutral equations.
- differential equations,
- second order neutral equation,
- distributed deviating arguments,
- oscillatory behavior,
- noncanonical case
Citation: Osama Moaaz, Asma Al-Jaser, Mohamed F. Abouelenein, Mona Anis. Optimized properties for noncanonical neutral differential equations with distributed deviating arguments and their oscillation analysis[J]. AIMS Mathematics, 2026, 11(6): 17838-17858. doi: 10.3934/math.2026727

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Abstract

This work develops new oscillation criteria for second‑order neutral differential equations with distributed deviating arguments. The analysis covers both the noncanonical case and the situation in which the coefficient of the neutral delay term exceeds one, settings that remain insufficiently addressed in the existing literature. The main contribution of this study is the derivation of several refined inequalities that strengthen the relation between the solution and its associated function. These improved relations allow us to establish sharper oscillation criteria, including a Kneser ‑type criterion and additional forms that extend and refine earlier approaches. Several examples are provided to apply the theoretical results and to compare them with related findings. The findings indicate that the developed framework offers a more sensitive and robust tool for detecting oscillatory behavior in this class of neutral equations.

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