This study is concerned with investigating the oscillatory properties of a general class of neutral differential equations. Neutral equations are characterized by being rich in both practical and theoretical aspects. We obtain criteria that guarantee the oscillation of solutions to a fourth-order neutral differential equation with multiple delays. Considering the canonical case, we obtain some new relations and inequalities that help in obtaining improved criteria. We use the reduction method to relate the oscillation of the studied equation to a first-order equation. We apply the results to a special case. Through this application, we evaluated the efficiency of the new results in the oscillation test compared to previous results in the literature.

In this paper, we study the oscillatory behavior of second-order differential equations. Using the comparison method, we obtain new oscillation criteria that improve the relevant results in the literature. Additionally, an example is given to illustrate the importance of the obtained oscillation criteria.

In this paper, we study the oscillation of a class of second-order nonlinear differential equations with mixed neutral terms in the non-canonical case. New criteria are derived that ensure the oscillation of the studied equation. The results obtained here greatly improve and extend some of the results reported in previous studies. To illustrate this, we present some examples.

Since differential equations play a major role in mathematics, physics, and engineering, the study of the oscillatory behavior of these equations is of great importance. In this paper, we apply the comparison method with first-order differential equations to study the oscillatory behavior of second-order differential equations. New oscillation criteria were obtained to improve some of the results of previous studies. Examples are included to illustrate the importance and novelty of the presented results.

In this study, we aim to contribute to the increasing interest in functional differential equations by obtaining new theorems for the oscillation of second-order neutral differential equations of mixed type in a non-canonical form. The results obtained here improve and extend those reported in the literature. The applicability of the results is illustrated by several examples.