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
Status
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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ZERO HUNGER2
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DECENT WORK AND ECONOMIC GROWTH8
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INDUSTRY, INNOVATION AND INFRASTRUCTURE9
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Documents

38

Citations

658

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13

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Documents

3

Citations

13

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Scholarly Output

28

Articles

27

Views / Downloads

10/1348

Supervised MSc Theses

0

Supervised PhD Theses

1

WoS Citation Count

367

Scopus Citation Count

527

Patents

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0

WoS Citations per Publication

13.11

Scopus Citations per Publication

18.82

Open Access Source

18

Supervised Theses

1

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: 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 - 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 - 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: 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.
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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: 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: 20
    Citation - Scopus: 33
    Function Bounds for Solutions of Volterra Integro Dynamic Equations on Time Scales
    (University of Szeged, 2010) Adivar M.
    Introducing shift operators on time scales we construct the integro-dynamic equation corresponding to the convolution type Volterra differential and difference equations in particular cases T = R and T = Z. Extending the scope of time scale variant of Gronwall's inequality we determine function bounds for the solutions of the integro dynamic equation.
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    Article
    Citation - WoS: 9
    Citation - Scopus: 13
    Inequalities and Exponential Stability and Instability in Finite Delay Volterra Integro-Differential Equations
    (Springer-Verlag Italia Srl, 2012) Adıvar, Murat; Raffoul, Youssef N.
    We use Liapunov functionals to obtain sufficient conditions that ensure exponential stability of the nonlinear Volterra integro- differential equation x(2) (t) = p(1)x(t) - integral(t)(t-iota) q(t,s)x(s)ds where the constant t is positive, the function p does not need to obey any sign condition and the kernel q is continuous. Our results improve the results obtained in literature even in the autonomous case. In addition, we give a new criteria for instability.