Improved Solution–Function Inequalities and Kneser-Type Oscillation Criteria for Noncanonical Neutral Differential Equations with Continuous Delay

This paper investigates the oscillatory behavior of second-order noncanonical neutral differential equations involving a neutral term with continuous delay and distributed deviating arguments. The main contribution is the establishment of a new and sharper relation between the solution and the corresponding neutral function, a problem that has not been addressed previously for noncanonical neutral equations with continuous delay. By combining iterative techniques with refined inequalities, we derive several new oscillation criteria, including Kneser-type conditions. The obtained results significantly extend the existing theory and improve a number of known oscillation tests in the literature. Illustrative examples and detailed comparisons with recent criteria demonstrate the effectiveness and superiority of the proposed approach in detecting oscillatory solutions.