Nonoscillatory Solutions for m -th-Order Nonlinear Neutral Differential Equations with General Delays: Fixed-Point Approach and Application

Mouataz Billah Mesmouli, Ioan-Lucian Popa () and Taher S. Hassan
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Mouataz Billah Mesmouli: Department of Mathematics, College of Science, University of Hail, Hail 2440, Saudi Arabia
Ioan-Lucian Popa: Department of Computing, Mathematics and Electronics, 1 Decembrie 1918 University of Alba Iulia, 510009 Alba Iulia, Romania
Taher S. Hassan: Department of Mathematics, College of Science, University of Hail, Hail 2440, Saudi Arabia

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

Abstract: This paper investigates the existence and uniqueness of bounded nonoscillatory solutions for two classes of m -th-order nonlinear neutral differential equations that incorporate both discrete and distributed delays. By applying Banach’s fixed-point theorem, we establish sufficient conditions under which such solutions exist. The results extend and generalize previous works by relaxing assumptions on the nonlinear terms and accommodating a wider range of feedback structures, including positive, negative, bounded, and unbounded cases. The mathematical framework is unified and applicable to a broad class of problems, providing a comprehensive treatment of neutral equations beyond the first or second order. To demonstrate the practical relevance of the theoretical findings, we analyze a delayed temperature control system as an application and provide numerical simulations to illustrate nonoscillatory behavior. This paper concludes with a discussion of analytical challenges, limitations of the numerical scope, and possible future directions involving stochastic effects and more complex delay structures.

Keywords: nonoscillatory; differential equations; neutral; fixed point; delay; control systems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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