An improved approach for analyzing oscillatory behavior in neutral differential equations with continuous delay

This study investigates the oscillatory behavior of solutions to functional differential equations that involve a neutral term with continuous delay. The main objective is to establish an improved relation between the solution and its associated function for this class of equations. Although several works have addressed similar improvements for other types of equations, no comparable results exist for the neutral equations considered here. To assess the impact of the refined relation, three methodologies are employed to derive new oscillation criteria: an extension of the Koplatadze approach, the Riccati transformation, and the comparison technique. Examples are provided to highlight the applicability of the new results and to compare them with previously established criteria. The comparisons show that the new criteria improve and extend the existing ones.