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Oscillatory Analysis of Third-Order Hybrid Trinomial Delay Differential Equations via Binomial Transform

Author

Listed:
  • Ganesh Purushothaman

    (Department of Mathematics, St. Joseph’s College of Engineering, Chennai 600119, India)

  • Ekambaram Chandrasekaran

    (Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Avadi, Chennai 600062, India)

  • George E. Chatzarakis

    (Department of Electrical and Electronic Engineering Educators, School of Pedagogical and Technological Education, Marousi, 15122 Athens, Greece)

  • Ethiraju Thandapani

    (Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai 600005, India)

Abstract

The oscillatory behavior of a class of third-order hybrid-type delay differential equations—used to model various real-world phenomena in fluid dynamics, control systems, biology, and beam deflection—is investigated in this study. A novel method is proposed, whereby these complex trinomial equations are reduced to a simpler binomial form by employing solutions of the corresponding linear differential equations. Through the use of comparison techniques and integral averaging methods, new oscillation criteria are derived to ensure that all solutions exhibit oscillatory behavior. These results are shown to extend and enhance existing theories in the oscillation analysis of functional differential equations. The effectiveness and originality of the proposed approach are illustrated by means of two representative examples.

Suggested Citation

  • Ganesh Purushothaman & Ekambaram Chandrasekaran & George E. Chatzarakis & Ethiraju Thandapani, 2025. "Oscillatory Analysis of Third-Order Hybrid Trinomial Delay Differential Equations via Binomial Transform," Mathematics, MDPI, vol. 13(15), pages 1-14, August.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:15:p:2520-:d:1718243
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    References listed on IDEAS

    as
    1. Irena Jadlovská & George E. Chatzarakis & Jozef Džurina & Said R. Grace, 2021. "On Sharp Oscillation Criteria for General Third-Order Delay Differential Equations," Mathematics, MDPI, vol. 9(14), pages 1-18, July.
    2. J. Džurina & B. Baculíková, 2012. "Oscillation and Asymptotic Behavior of Higher-Order Nonlinear Differential Equations," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-9, July.
    3. B. Baculíková, 2011. "Properties of Third-Order Nonlinear Functional Differential Equations with Mixed Arguments," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-15, March.
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