Browsing by Author "Koyuncuoglu, Halis Can"

Now showing 1 - 7 of 7

Citation - WoS: 5
Citation - Scopus: 4
Almost Automorphic Solutions of Delayed Neutral Dynamic Systems on Hybrid Domains
(Univ Belgrade, Fac Electrical Engineering, 2016) Adıvar, Murat; Koyuncuoglu, Halis Can; Raffoul, Youssef N.
We study the existence of almost automorphic solutions of the delayed neutral dynamic system on hybrid domains that are additively periodic. We use exponential dichotomy and prove the uniqueness of projector of exponential dichotomy to obtain some limit results leading to sufficient conditions for existence of almost automorphic solutions to neutral system. Unlike the existing literature we prove our existence results without assuming boundedness of the coefficient matrices in the system. Hence, we significantly improve the results in the existing literature. Finally, we also provide an existence result for almost periodic solutions of the system.
Citation - WoS: 15
Citation - Scopus: 13
Almost Automorphic Solutions of Discrete Delayed Neutral System
(Academic Press Inc Elsevier Science, 2016) Adıvar, Murat; Koyuncuoglu, Halis Can
We study almost automorphic solutions of the discrete delayed neutral dynamic system x(t + 1) = A(t)x(r) + Delta Q(t, x(t - g(t)) + G(t, x(t), x(t - g(t)) by means of a fixed point theorem due to Krasnoselskii. Using discrete variant of exponential dichotomy and proving uniqueness of projector of discrete exponential dichotomy we invert the equation and obtain some limit results leading to sufficient conditions for the existence of almost automorphic solutions of the neutral system. Unlike the existing literature we prove our existence results without assuming boundedness of inverse matrix A (t)(-1). Hence, we significantly improve the results in the existing literature. We provide two examples to illustrate effectiveness of our results. Finally, we also provide an existence result for almost periodic solutions of the system. (C) 2015 Elsevier Inc. All rights reserved.
Citation - WoS: 2
Asymptotic Constancy for Solutions of Abstract Non-Linear Fractional Equations With Delay and Generalized Hilfer ( A, B, A )- Derivatives
(Pergamon-elsevier Science Ltd, 2025) Kostic, Marko; Koyuncuoglu, Halis Can; Katican, Tugce
In this paper, we investigate the asymptotic constancy for solutions of abstract non-linear fractional differential (difference) equations with delay and generalized Hilfer ( a, b, a )- derivatives. Our results are applicable to the abstract fractional functional equations with the usually considered Riemann-Liouville, Caputo, Hilfer and Prabhakar derivatives.
Citation - WoS: 7
Citation - Scopus: 7
Existence of Periodic Solutions in Shifts Delta(+/-) for Neutral Nonlinear Dynamic Systems
(Elsevier Science Inc, 2014) Adıvar, Murat; Koyuncuoglu, Halis Can; Raffoul, Youssef N.
This paper focuses on the existence of a periodic solution of the delay neutral nonlinear dynamic systems x(Delta)(t) = A(t)x(t) + Q(Delta)(t, x(delta (-) (s, t))) + G(t, x(t), x(delta (-) (s, t))). In our analysis, we utilize a new periodicity concept in terms of shifts operators, which allows us to extend the concept of periodicity to time scales where the additivity requirement t +/- T is an element of T for all t is an element of T and for a fixed T > 0, may not hold. More importantly, the new concept will easily handle time scales that are not periodic in the conventional way such as; (q(z)) over bar and boolean OR(infinity)(k-1) [3(+/- k), 2.3(+/- k)] boolean OR {0}. Hence, we will develop the tool that enables us to investigate the existence of periodic solutions of q-difference systems. Since we are dealing with systems, in order to convert our equation to an integral systems, we resort to the transition matrix of the homogeneous Floquet system y(Delta)(t) = A(t)y(t) and then make use of Krasnoselskii's fixed point theorem to obtain a fixed point. (C) 2014 Elsevier Inc. All rights reserved.
Citation - WoS: 11
Citation - Scopus: 11
Floquet Theory Based on New Periodicity Concept for Hybrid Systems Involving Q-Difference Equations
(Elsevier Science Inc, 2016) Adıvar, Murat; Koyuncuoglu, Halis Can
Using the new periodicity concept based on shifts, we construct a unified Floquet theory for homogeneous and nonhomogeneous hybrid periodic systems on domains having continuous, discrete or hybrid structure. New periodicity concept based on shifts enables the construction of Floquet theory on hybrid domains that are not necessarily additive periodic. This makes periodicity and stability analysis of hybrid periodic systems possible on non-additive domains. In particular, this new approach can be useful to know more about Floquet theory for linear q-difference systems defined one (q(Z)) over bar := (q(n) : n is an element of Z} U {0} where q > 1. By constructing the solution of matrix exponential equation we establish a canonical Floquet decomposition theorem. Determining the relation between Floquet multipliers and Floquet exponents, we give a spectral mapping theorem on closed subsets of reals that are periodic in shifts. Finally, we show how the constructed theory can be utilized for the stability analysis of dynamic systems on periodic time scales in shifts. (C) 2015 Elsevier Inc. All rights reserved.
Citation - WoS: 7
Citation - Scopus: 10
Periodic and Asymptotically Periodic Solutions of Systems of Nonlinear Difference Equations With Infinite Delay
(Taylor & Francis Ltd, 2013) Adıvar, Murat; Koyuncuoglu, Halis Can; Raffoul, Youssef N.
In this paper we study the existence of periodic and asymptotically periodic solutions of a system of nonlinear Volterra difference equations with infinite delay. By means of fixed point theory, we furnish conditions that guarantee the existence of such periodic solutions.
Q-Floquet Theory and Its Extensions To Time Scales Periodic in Shifts
(İzmir Ekonomi Üniversitesi, 2016) Koyuncuoglu, Halis Can; Adıvar, Murat
Bu tezde q-fark sistemlerinin Floquet teorisi çarpımsal periyodiklik kavramı kullanılarak incelenmiştir. Floquet ayrışma teoremi üstel matris fonksiyonu denkleminin çözümünün varlığı ispatlanarak verilmiştir. Homojen ve homojen olmayan q-Floquet fark sistemleri incelenerek, periyodik çözümün varlığı için gerek yeter koşullar gösterilmiştir. Ayrıca, Floquet çarpanları ve Floquet kuvvetleri arasında kurulan ilişkinin ışığında elde edilen sonuçlar kararlılık analizinde kullanılmış tır. Tezin kalan kısmında, q-Floquet teorisi zaman skalalarında kaydırma operatörlerine bağlı olarak tanımlanan yeni periyodiklik kavramıyla genelleştirilmiştir. Bu yaklaşım dinamik sistemlerin Floquet teorisinin toplamsallık koşulu aranmaksızın daha genel tanım aralıklarında tartışılmasına imkan tanımıştır. Genelleştirilen sonuçlar Floquet teorisine daha geniş bir açıdan bakılmasını sağlayıp, literatürdeki şu ana kadar Floquet teorisi üzerine yapılmış çalışmalar içerisinde en genel olanlarıdır.