New comparison theorems for testing the oscillation of solutions of fourth-order differential equations with a variable argument

In this study, we establish new oscillation criteria for the fourth-order delay differential equation. Our main objective is to build upon recent advancements in the study of the oscillatory behavior of second-order equations and extend these findings to higher-order equations. Although fourth-order equations have numerous applications, their study presents significant analytical challenges due to the complex nature of their solutions, which we will discuss in this study. We use the comparison technique with first-order equations in several approaches. Our results show an improvement in the oscillation test due to the development of some monotonic and asymptotic properties of positive solutions. We present a comparison of the new criteria to test their effectiveness, as well as a comparison with previous studies to illustrate the novelty.