Adivar, Murat

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Profile URL
https://hdl.handle.net/20.500.14365/7192
Name Variants
Adıvar, Murat
Adivar, M
AdIvar, Murat
Advar, Murat
Job Title
Email Address
murat.adivar@ieu.edu.tr
Main Affiliation
02.02. Mathematics
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Former Staff
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ORCID ID
https://orcid.org/0000-0002-9707-2005
Scopus Author ID
55913381700
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Google Scholar ID
VPZYO7cAAAAJ
WoS Researcher ID
IXL-6052-2023

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Documents

38

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658

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Scholarly Output

28

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WoS Citation Count

367

Scopus Citation Count

527

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Scopus Citations per Publication

18.82

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18

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JournalCount
Applıed Mathematıcs And Computatıon3
Mathematıcal And Computer Modellıng2
Computers & Mathematıcs Wıth Applıcatıons2
Electronic Journal of Qualitative Theory of Differential Equations2
Communications in Applied Analysis1
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Now showing 1 - 10 of 28
  • Thumbnail Image
    Article
    Citation - WoS: 37
    Citation - Scopus: 42
    Spectral Analysis of Q-Difference Equations With Spectral Singularities
    (Pergamon-Elsevier Science Ltd, 2006) Adivar, M; Bohner, M
    In this paper we investigate the eigenvalues and the spectral singularities of non-selfadjoint q-difference equations of second order with spectral singularities. (c) 2005 Elsevier Ltd. All rights reserved.
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    Doctoral Thesis
    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.
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    Article
    Citation - WoS: 3
    Citation - Scopus: 6
    Oscillatory Behavior of Solutions of Third-Order Delay and Advanced Dynamic Equations
    (Springer, 2014) Adıvar, Murat; Akin, Elvan; Higgins, Raegan
    In this paper, we consider oscillation criteria for certain third-order delay and advanced dynamic equations on unbounded time scales. A time scale T is a nonempty closed subset of the real numbers. Examples will be given to illustrate some of the results.
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    Article
    Citation - WoS: 20
    Citation - Scopus: 23
    Separate Contraction and Existence of Periodic Solutions in Totally Nonlinear Delay Differential Equations
    (Hacettepe University, 2012) Adivar M.; Islam M.N.; Raffoul Y.N.
    In this study, we employ the fixed point theorem of Krasnoselskii and the concepts of separate and large contractions to show the existence of a periodic solution of a highly nonlinear delay differential equation. Also, we give a classification theorem providing sufficient conditions for an operator to be a large contraction, and hence, a separate contraction. Finally, under slightly different conditions, we obtain the existence of a positive periodic solution.
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    Article
    Citation - Scopus: 19
    Shift Operators and Stability in Delayed Dynamic Equations
    (Rendiconti del Seminario Matematico, 2010) Adivar M.; Raffoul Y.N.
    In this paper, we use what we call the shift operator so that general delay dynamic equations of the form x?(t) = a(t)x(t)+b(t)x(?- (h,t)) ??-(h,t), t ? (t 0,?) ?T can be analyzed with respect to stability and existence of solutions. By means of the shift operators, we define a general delay function opening an avenue for the construction of Lya-punov functional on time scales. Thus, we use the Lyapunov's direct method to obtain inequalities that lead to stability and instability. Therefore, we extend and unify stability analysis of delay differential, delay difference, delay h-difference, and delay q-difference equations which are the most important particular cases of our delay dynamic equation.
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    Article
    Citation - WoS: 4
    Citation - Scopus: 2
    Inequalities and Exponential Decay in Time Varying Delay Differential Equations
    (Pergamon-Elsevier Science Ltd, 2011) Adivar, Murat; Raffoul, Youssef N.
    We use Lyapunov functionals to obtain sufficient conditions that guarantee exponential decay of solutions to zero of the time varying delay differential equation x'(t) = b(t) x(t) - a(t) x(t - h(t)). The highlights of the paper are allowing b( t) to change signs and the delay to vary with time. In addition, we obtain a criterion for the instability of the zero solution. Moreover, by comparison to existing literature we show effectiveness of our results. (C) 2011 Elsevier Ltd. All rights reserved.
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    Article
    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.
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    Article
    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.
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    Article
    Citation - WoS: 21
    Citation - Scopus: 28
    Stability and Periodicity in Dynamic Delay Equations
    (Pergamon-Elsevier Science Ltd, 2009) Adıvar, Murat; Raffoul, Youssef N.
    Let T be an arbitrary time scale that is unbounded above. By means of a variation of Lyapunov's method and contraction mapping principle this paper handles asymptotic stability of the zero solution of the completely delayed dynamic equations x(Delta)(t) = -a(t)x(delta(t))delta(Delta)d(t). Moreover, if T is a periodic time scale, then necessary conditions are given for the existence of a unique periodic solution of the above mentioned equation. (c) 2009 Elsevier Ltd. All rights reserved.
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    Article
    Citation - WoS: 14
    Citation - Scopus: 11
    Quadratic Pencil of Difference Equations: Jost Solutions, Spectrum, and Principal Vectors
    (Natl Inquiry Services Centre Pty Ltd, 2010) Adıvar, Murat
    In this paper, a quadratic pencil of Schrodinger type difference operator L is taken under investigation to provide a general perspective for the spectral analysis of non-selfadjoint difference equations of second order. Introducing Jost-type solutions, structure and quantitative properties of the spectrum of L are investigated. Therefore, a discrete analog of the theory in [6] and [7] is developed. In addition, several analogies are established between difference and q-difference cases. Finally, the principal vectors of L are introduced to lay a groundwork for the spectral expansion.