(untitled) (European Journal of Pure and Applied Mathematics, 2025)
In this paper, we investigate the oscillatory properties of fourth-order neutral delay differential equation solutions in the canonical situation. To our knowledge, this equation has received minimal research. We prove new improved features and relationships for the solution and the accompanying function. Based on these relationships, oscillation theorems were developed that guarantee oscillation of all solutions to the considered equation. The comparison principle used in our results is one of the most significant methods for investigating the oscillatory behavior of delay differential equations. The findings of our study extend and develop a number of previous findings in the literature.