Nonlinear oscillation analysis of delay differential equations with mixed neutral terms

Fahd Masood; Mohammed N. Alshehri; Iambor Loredana Florentina; A. F. Aljohani; Omar Bazighifan; Fahd Masood; Mohammed N. Alshehri; Iambor Loredana Florentina; A. F. Aljohani; Omar Bazighifan

doi:10.3934/math.20251090

AIMS Mathematics

2025, Volume 10, Issue 10: 24580-24601. doi: 10.3934/math.20251090

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Nonlinear oscillation analysis of delay differential equations with mixed neutral terms

1.
Department of Mathematics, Faculty of Education and Science, University of Saba Region, Marib, Yemen
2.
Department of Mathematics, College of Arts & Science, Najran University, Najran, Saudi Arabia
3.
Department of Mathematics and Computer Science, University of Oradea, University Street, 410087 Oradea, Romania
4.
Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk, Saudi Arabia
5.
Department of Mathematics, Faculty of Education, Seiyun University, Hadhramout 50512, Yemen
6.
Jadara Research Center, Jadara University, Irbid 21110, Jordan

Received: 28 September 2025 Revised: 17 October 2025 Accepted: 22 October 2025 Published: 28 October 2025
MSC : 34C10, 34K11

This paper investigates novel sufficient conditions for the oscillatory behavior of fourth-order nonlinear differential equations with mixed neutral terms. By employing refined Riccati transformation techniques and advanced analytical approaches, we establish extended criteria that enrich the theoretical understanding of oscillation phenomena within this class of neutral differential equations. The proposed results significantly improve upon previously known conditions in the literature. Moreover, illustrative numerical examples are provided to demonstrate the applicability and sharpness of the obtained criteria. The findings contribute to the broader framework of nonlinear analysis and offer valuable insights into the oscillatory dynamics of functional differential equations with delay and neutral terms.
- oscillation criteria,
- nonlinear equations,
- delay differential equations,
- mixed neutral terms,
- canonical form,
- fourth-order
Citation: Fahd Masood, Mohammed N. Alshehri, Iambor Loredana Florentina, A. F. Aljohani, Omar Bazighifan. Nonlinear oscillation analysis of delay differential equations with mixed neutral terms[J]. AIMS Mathematics, 2025, 10(10): 24580-24601. doi: 10.3934/math.20251090

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Abstract

This paper investigates novel sufficient conditions for the oscillatory behavior of fourth-order nonlinear differential equations with mixed neutral terms. By employing refined Riccati transformation techniques and advanced analytical approaches, we establish extended criteria that enrich the theoretical understanding of oscillation phenomena within this class of neutral differential equations. The proposed results significantly improve upon previously known conditions in the literature. Moreover, illustrative numerical examples are provided to demonstrate the applicability and sharpness of the obtained criteria. The findings contribute to the broader framework of nonlinear analysis and offer valuable insights into the oscillatory dynamics of functional differential equations with delay and neutral terms.

References

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