Conditions for the Oscillation of Solutions to Neutral Differential Equations of Higher Order

In this research, we applied three techniques-the comparison technique, the Riccati technique, and the integral averages technique to analyze and establish various conditions and properties associated with the oscillatory behavior of even-order neutral differential equations. These findings contribute to a better understanding of the dynamics of such equations. To demonstrate the efficacy of these new conditions and properties, we present illustrative examples. This study offers valuable insights into the behavior of neutral differential equations, advancing our knowledge in this field.