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Fourth-Order Neutral Differential Equation: A Modified Approach to Optimizing Monotonic Properties

Author

Listed:
  • Amany Nabih

    (Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
    Department of Mathematics and Basic Sciences, Higher Future Institute of Engineering and Technology, Mansoura 35516, Egypt)

  • Osama Moaaz

    (Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
    Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy)

  • Sameh S. Askar

    (Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia)

  • Ahmad M. Alshamrani

    (Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia)

  • Elmetwally M. Elabbasy

    (Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt)

Abstract

In this article, we investigate some qualitative properties of solutions to a class of functional differential equations with multi-delay. Using a modified approach, we first derive a number of optimized relations and inequalities that relate the solution x s to its corresponding function z s and its derivatives. After classifying the positive solutions, we follow the Riccati approach and principle of comparison, where fourth-order differential equations are compared with first-order differential equations to obtain conditions that exclude the positive solutions. Then, we introduce new oscillation conditions. With regard to previous relevant results, our results are an extension and complement to them. This work has theoretical significance in that it uncovers some new relationships that aid in developing the oscillation theory of higher-order equations in addition to the applied relevance of neutral differential equations.

Suggested Citation

  • Amany Nabih & Osama Moaaz & Sameh S. Askar & Ahmad M. Alshamrani & Elmetwally M. Elabbasy, 2023. "Fourth-Order Neutral Differential Equation: A Modified Approach to Optimizing Monotonic Properties," Mathematics, MDPI, vol. 11(20), pages 1-15, October.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:20:p:4380-:d:1264558
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    References listed on IDEAS

    as
    1. Irena Jadlovská, 2021. "New Criteria for Sharp Oscillation of Second-Order Neutral Delay Differential Equations," Mathematics, MDPI, vol. 9(17), pages 1-23, August.
    2. Agarwal, Ravi P. & Zhang, Chenghui & Li, Tongxing, 2016. "Some remarks on oscillation of second order neutral differential equations," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 178-181.
    3. Osama Moaaz & Ali Muhib & Saud Owyed & Emad E. Mahmoud & Aml Abdelnaser & Kottakkaran Sooppy Nisar, 2021. "Second-Order Neutral Differential Equations: Improved Criteria for Testing the Oscillation," Journal of Mathematics, Hindawi, vol. 2021, pages 1-7, February.
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