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

Ganesh Purushothaman, Ekambaram Chandrasekaran, George E. Chatzarakis () and Ethiraju Thandapani
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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

Mathematics, 2025, vol. 13, issue 15, 1-14

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.

Keywords: third-order differential equation; positive and negative terms; neutral; trinomial equation; oscillation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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