الفهرس 
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Abstract
Adynamic equation is a mathematical equation that describes the behavior of a dynamic system over time. It represents the relationships between variables and their rates of change, allowing us to understand how the system evolves and predict its future states. These equations find applications in diverse fields like physics, engineering, economics, and biology. Recent research has shown a growing interest in understanding the asymptotic and oscillatory properties of a fundamental type of dynamic equation known as differential equations, with a particular emphasis on functional differential equations. This thesis will delve into the investigation of main properties of functional differential equations, focusing on the asymptotic and oscillatory behavior of specific types, notably delay differential equations and neutral differential equations of different orders. To achieve this objective, we will delve into a comprehensive analysis of these equations, seeking to understand their behavior under different conditions. The findings of this study are expected to contribute valuable insights to the broader understanding of functional differential equations and their significance in dynamic systems. The thesis comprises five chapters : Chapter 1 serves as an introduction, presenting basic definitions, results, and theorems that are foundational for the subsequent chapters. In Chapter 2, we explore the oscillation properties of a third-order quasilinear delay differential equation in the canonical case. New conditions are introduced to determine whether the solutions oscillate or converge to zero. Chapter 3 delves into the asymptotic properties of positive solutions for quasilinear fourth-order delay differential equations in the canonical case. Using the comparison method, we establish conditions to exclude positive solutions and prove theorems ensuring the oscillatory behavior of the studied equation. Chapter 4 examines the oscillatory properties of the fourth-order Emden-Fowler differential equation, specifically when including a sublinear neutral term in the canonical case. Multiple theorems, employing the Riccati technique, introduce conditions eliminating positive solutions and establish oscillation criteria. In Chapter 5, we investigate the asymptotic properties of positive solutions related to even-order neutral differential equations in the non-canonical case. New conditions are introduced to exclude positive solutions, employing a combination of the comparison technique and the Riccati method. Fundamental theorems reveal the oscillatory nature of all solutions under specific criteria. Through the rigorous examination of these equations, our research seeks to provide a deeper understanding of their behavior, which may have potential applications in various fields such as physics, engineering, and biology. Overall, the thesis contributes to understanding the oscillatory behavior of solutions of differential equations of higher order and provides new criteria and results that can be applied to various types of differential equations.