Fourth-order differential equations with neutral delay: Investigation of monotonic and oscillatory features

For fourth-order neutral differential equations (NDE) in the canonical case, we present new relationships between the solution and its corresponding function in two casses: $ p < 1 $ and $ p > 1 $. Through these relationships, we discover new monotonic properties for this equation of fourth order. Using the new relationships and properties, we derive some oscillation conditions for the equation under study. By using the Comparison and Ricatti technique, the positive solutions are excluded by providing some conditions. Lastly, we provide examples and review previous theorems from the literature to compare our findings.