الفهرس 
1 PreliminariesOnly 14 pages are availabe for public view
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Abstract
This thesis consists of five chapters :
Chapter 1, is an introductory chapter that contains the basic concepts of studying the oscillation of solutions for functional differential equations as well as some previous results in studying the oscillation of second order neutral differential equations.
In Chapter 2, we give an introduction to the theory of dynamic equations on time scales, differentiation and integration, and some examples of time scales. Moreover, we present various properties of generalized exponential function on time scales. Additionally, some previous studies for the oscillation theory of second order neutral dynamic equations and second order dynamic equations with damping on time scales are presented.
In Chapter 3, we establish some new oscillation criteria for the second-order nonlinear neutral dynamic equation with mixed arguments on a time scale T
(〖r(t)[(x(t)+p_1 (t)x(η_1 (t))+p_2 (t)x(η_2 (t)))〗^∆ ]^γ )^∆+f(t,x(τ_1 (t)))+g(t,x(τ_2 (t)))=0,
The results of this chapter generalize and extend the results of Tao Ji et al. [29], and published in: Journal of Basic and Applied Research International 17(1)(2016) 49-66. [5].
In Chapter 4, we present some new oscillation results for the second-order nonlinear mixed neutral dynamic equation with non positive neutral term on a time scale T
(〖r(t)[(x(t) 〖-p〗_1 (t)x(η_1 (t))+p_2 (t)x(η_2 (t)))〗^∆ ]^γ )^∆+f(t,x(τ_1 (t)))+g(t,x(τ_2 (t)))=0,
Our results not only generalize some existing results in [22], but also can be applied to some oscillation problems that do not covered before. Also, we give some examples to explain our results. The results of this chapter published in: Academic Journal of Applied Mathematical Sciences 3 (2) (2017)8-20 [6]
Chapter 5 is concerned with the oscillatory behavior of all solutions of the second-order mixed nonlinear neutral dynamic equation with damping on a time scale T
(〖r(t)Φ(z〗^∆ (t)))^∆+p(t) 〖Φ(z〗^∆ (t))+f(t,x(τ_1 (t)))+g(t,x(τ_2 (t)))=0,
Where
Φ(s)=〖⎹ s⎹〗^(γ-1) s and z(t)= x(t)+p_1 (t)x(η_1 (t))+p_2 (t)x(η_2 (t)). Our results generalize the results of [22] and [30] which are considered as special cases of our results when taking α = β = γ, p(t) = p2(t) = 0 and considering either g(t,x(τ_2 (t)))=0 or f(t,x(τ_1 (t)))=0. Also, we introduce an illustrated example.