Novel oscillation criteria for general third-order nonlinear neutral differential equations

This research aims to introduce new criteria that guarantee the oscillation of all solutions to third-order nonlinear neutral differential equations in their canonical form. The proposed methodology integrates the comparison principle with first-order differential equations and employs the Riccati substitution technique, which simplifies the complex structure of the equations and transforms them into more analyzable forms. This approach contributes to establishing general and precise oscillation conditions, representing an extension and improvement over previously published work in this field. It is important to note that this study is purely analytical, focusing on the derivation of oscillatory properties and theoretical criteria. To validate the applicability of the results, three numerical examples are provided, demonstrating the capability of the proposed criteria to verify the oscillation of solutions and highlighting both the theoretical and practical significance of the methodology.