Optimized properties for noncanonical neutral differential equations with distributed deviating arguments and their oscillation analysis

This work develops new oscillation criteria for second‑order neutral differential equations with distributed deviating arguments. The analysis covers both the noncanonical case and the situation in which the coefficient of the neutral delay term exceeds one, settings that remain insufficiently addressed in the existing literature. The main contribution of this study is the derivation of several refined inequalities that strengthen the relation between the solution and its associated function. These improved relations allow us to establish sharper oscillation criteria, including a Kneser ‑type criterion and additional forms that extend and refine earlier approaches. Several examples are provided to apply the theoretical results and to compare them with related findings. The findings indicate that the developed framework offers a more sensitive and robust tool for detecting oscillatory behavior in this class of neutral equations.