Browsing by Author "Gozen, Melek"

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Boundedness of Vector Linéard Equation With Multiple Variable Delays
(Mdpi, 2024) Gozen, Melek
In this article, we consider a system of ordinary differential equations (ODEs) of second order with two variable time delays. We obtain new conditions for uniform ultimate bounded (UUB) solutions of the considered system. The technique of the proof is based on the Lyapunov-Krasovskii functional (LKF) method using a new LKF. The main result of this article extends and improves a recent result for ODEs of second order with a constant delay to a more general system of ODEs of second order with two variable time delays. In this particular case, we also give a numerical example to verify the application of the main result of this article.
Convergence of Solutions To a Certain Vector Differential Equation of Third Order
(Hindawi Publishing Corporation, 2014) Tunc, Cemil; Gozen, Melek
We give some sufficient conditions to guarantee convergence of solutions to a nonlinear vector differential equation of third order. We prove a new result on the convergence of solutions. An example is given to illustrate the theoretical analysis made in this paper. Our result improves and generalizes some earlier results in the literature.
A New Result on the Exponential Stability of Solutions of Non-Linear Neutral Type Periodic Systems With Variable Delay
(Lebanese Univ, 2021) Gozen, Melek; Tunc, Cemil
In this work, we consider a nonlinear time-varying delay system of neutral type differential equations with periodic coefficients and we obtain new sufficient conditions to ensure exponentially stability of zero solution of this system. The Lyapunov-Krasovskii functional approach is useful as a basic tool to prove the main general result of this paper.
On the Asymptotic Stability a System With Nonlinear Perturbations and Constant Delay
(Prairie View A & M Univ, dept Mathematics, 2022) Gozen, Melek
In this paper, we consider a nonlinear perturbed system of neutral delay integro-differential equations (NDIDEs). We prove two new theorems, Theorems 1 and 2, such that these theorems include sufficient conditions and are related to asymptotical stability of zero solution of the perturbed system of NDIDEs. The technique of the proofs depends upon the definitions of two new and more suitable Lyapunov-Krasovskii functionals (LKFs). When we compared the results of this paper with those found in the literature, our results improve and extend some classical results, and contribute new contents to the topic of NDIDEs and to the profession.
On the Behaviors of Solutions To a Functional Differential Equation of Neutral Type With Multiple Delays
(Lebanese Univ, 2019) Gozen, Melek; Tunc, Cemil
We consider a linear functional differential equation of first order and neutral type with multiple constant delays and present a functional Lyapunov approach to square integrability and asymptotic analysis of solutions of the equation considered. Consequently explicit criteria are derived for square integrability and asymptotic analysis of solutions of the equation considered. A discussion of the result obtained and an illustrative example are given. The result given extends and improves some found in the literature.
On the Existence and Uniqueness of Positive Periodic Solutions of Neutral Differential Equations
(Biemdas Acad Publishers inc, 2023) Gozen, Melek
In this paper, we investigate a nonlinear neutral differential equation of first order with iterative terms and constant time delays. We obtain new results on the existence and uniqueness of positive periodic solutions of the nonlinear neutral differential equation such that the solution depends on the functions of that the nonlinear neutral differential equation. The proof of the new results depends on some fixed point theorems and the Green's functions. We also provide a numerical example to demonstrate the conditions of the new results can be satisfied and applied.
Stability and Uniform Boundedness in Multidelay Functional Differential Equations of Third Order
(Hindawi Ltd, 2013) Tunc, Cemil; Gozen, Melek
We consider a nonautonomous functional differential equation of the third order with multiple deviating arguments. Using the Lyapunov-Krasovskii functional approach, we give certain sufficient conditions to guarantee the asymptotic stability and uniform boundedness of the solutions.
Stability in Functional Integro-Differential Equations of Second Order With Variable Delay
(inst Teknologi Bandung, 2017) Gozen, Melek; Tunc, Cemil
In this paper, we investigate the stability of the zero solution of an integro-differential equation of the second order with variable delay. By means of the fixed point theory and an exponential weighted metric, we find sufficient conditions under which the zero solution of the equation considered is stable.