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Peer-reviewedCC BY 4.0Axioms

Improved Solution–Function Inequalities and Kneser-Type Oscillation Criteria for Noncanonical Neutral Differential Equations with Continuous Delay

  • Osama Moaaz1,2
  • Asma Al-Jaser3
  1. 1Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia
  2. 2Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
  3. 3Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
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Abstract

This paper investigates the oscillatory behavior of second-order noncanonical neutral differential equations involving a neutral term with continuous delay and distributed deviating arguments. The main contribution is the establishment of a new and sharper relation between the solution and the corresponding neutral function, a problem that has not been addressed previously for noncanonical neutral equations with continuous delay. By combining iterative techniques with refined inequalities, we derive several new oscillation criteria, including Kneser-type conditions. The obtained results significantly extend the existing theory and improve a number of known oscillation tests in the literature. Illustrative examples and detailed comparisons with recent criteria demonstrate the effectiveness and superiority of the proposed approach in detecting oscillatory solutions.

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Cite

BibTeXRIS
BibTeX
@article{moaaz2026improved,
  title = {{Improved Solution–Function Inequalities and Kneser-Type Oscillation Criteria for Noncanonical Neutral Differential Equations with Continuous Delay}},
  author = {Osama Moaaz and Asma Al-Jaser},
  journal = {Axioms},
  year = {2026},
  month = oct,
  doi = {10.3390/axioms15110799},
  url = {https://www.mdpi.com/2075-1680/15/11/799},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Improved Solution–Function Inequalities and Kneser-Type Oscillation Criteria for Noncanonical Neutral Differential Equations with Continuous Delay
AU  - Osama Moaaz
AU  - Asma Al-Jaser
PY  - 2026
DA  - 2026/10/27
JO  - Axioms
DO  - 10.3390/axioms15110799
UR  - https://www.mdpi.com/2075-1680/15/11/799
AB  - This paper investigates the oscillatory behavior of second-order noncanonical neutral differential equations involving a neutral term with continuous delay and distributed deviating arguments. The main contribution is the establishment of a new and sharper relation between the solution and the corresponding neutral function, a problem that has not been addressed previously for noncanonical neutral equations with continuous delay. By combining iterative techniques with refined inequalities, we derive several new oscillation criteria, including Kneser-type conditions. The obtained results significantly extend the existing theory and improve a number of known oscillation tests in the literature. Illustrative examples and detailed comparisons with recent criteria demonstrate the effectiveness and superiority of the proposed approach in detecting oscillatory solutions.
SN  - 2075-1680
ER  -