Oscillation of Second-Order Noncanonical Advanced Type Neutral Differential Equations

This paper establishes new oscillation criteria for a specific class of second-order nonlinear noncanonical neutral differential equations that incorporate an advanced neutral argument. Rather than analyzing the equation in its initial noncanonical state, the study introduces a transformation technique utilizing an auxiliary function to convert the system into an equivalent canonical form. Following this transformation, integral averaging techniques are deployed to derive sufficient conditions that guarantee oscillation. Notably, the methodology comprehensively addresses both delayed and advanced cases of the argument. The resulting criteria extend and complement several established findings in the literature governing noncanonical neutral differential equations. Finally, the paper includes practical examples to demonstrate the applicability and effectiveness of the primary theoretical advancements.