Özbekler, Abdullah

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https://hdl.handle.net/20.500.14411/7654
Name Variants
Abdullah, Özbekler
A., Ozbekler
Ozbekler, Abdullah
O., Abdullah
O.,Abdullah
Abdullah, Ozbekler
A.,Ozbekler
Ozbekler,A.
Ö.,Abdullah
Özbekler,A.
A.,Özbekler
Özbekler, Abdullah
Ozbekler, A.
Oezbekler, A.
Job Title
Profesör Doktor
Email Address
abdullah.ozbekler@atilim.edu.tr
Main Affiliation
Mathematics
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Former Staff
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Scholarly Output

43

Articles

40

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1/0

Supervised MSc Theses

0

Supervised PhD Theses

0

WoS Citation Count

273

Scopus Citation Count

339

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0

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0

WoS Citations per Publication

6.35

Scopus Citations per Publication

7.88

Open Access Source

16

Supervised Theses

0

JournalCount
Mathematical Methods in the Applied Sciences6
Applied Mathematics and Computation4
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas3
Journal of Function Spaces2
Applied Mathematics Letters2
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Now showing 1 - 10 of 43
  • Thumbnail Image
    Article
    Citation - WoS: 22
    Citation - Scopus: 21
    Principal and Nonprincipal Solutions of Impulsive Differential Equations With Applications
    (Elsevier Science inc, 2010) Ozbekler, A.; Zafer, A.
    We introduce the concept of principal and nonprincipal solutions for second order differential equations having fixed moments of impulse actions is obtained. The arguments are based on Polya and Trench factorizations as in non-impulsive differential equations, so we first establish these factorizations. Making use of the existence of nonprincipal solutions we also establish new oscillation criteria for nonhomogeneous impulsive differential equations. Examples are provided with numerical simulations to illustrate the relevance of the results. (C) 2010 Elsevier Inc. All rights reserved.
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    Article
    Citation - WoS: 4
    Citation - Scopus: 6
    On the Oscillation of Even-Order Nonlinear Differential Equations With Mixed Neutral Terms
    (Hindawi Ltd, 2021) Kaabar, Mohammed K. A.; Özbekler, Abdullah; Grace, Said R.; Alzabut, Jehad; Ozbekler, Abdullah; Siri, Zailan; Özbekler, Abdullah; Mathematics; Mathematics
    The oscillation of even-order nonlinear differential equations (NLDiffEqs) with mixed nonlinear neutral terms (MNLNTs) is investigated in this work. New oscillation criteria are obtained which improve, extend, and simplify the existing ones in other previous works. Some examples are also given to illustrate the validity and potentiality of our results.
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    Article
    Citation - Scopus: 2
    Wong’s Oscillation Theorem for the Second-Order Delay Differential Equations
    (Springer New York LLC, 2017) Özbekler,A.; Zafer,A.
    [No abstract available]
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    Article
    New Criteria on Oscillatory and Asymptotic Behavior of Third-Order Nonlinear Dynamic Equations with Nonlinear Neutral Terms
    (MDPI, 2021) Ozbekler, Abdullah; Grace, Said R.; Alzabut, Jehad
    In the paper, we provide sufficient conditions for the oscillatory and asymptotic behavior of a new type of third-order nonlinear dynamic equations with mixed nonlinear neutral terms. Our theorems not only improve and extend existing theorems in the literature but also provide a new approach as far as the nonlinear neutral terms are concerned. The main results are illustrated by some particular examples.
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    Article
    Forced Oscillation of Delay Difference Equations Via Nonprincipal Solution
    (Wiley, 2018) Ozbekler, Abdullah
    In this paper, we obtain a new oscillation result for delay difference equations of the form Delta(r(n)Delta x(n)) + a(n)x(tau n) = b(n); n is an element of N under the assumption that corresponding homogenous equation Delta(r(n)Delta z(n)) + a(n)z(n+1) = 0; n is an element of N is nonoscillatory, where tau(n) <= n + 1. It is observed that the oscillation behaviormay be altered due to presence of the delay. Extensions to forced Emden-Fowler-type delay difference equations Delta(r(n)Delta x(n)) + a(n)vertical bar x(tau n)vertical bar(alpha-1)x(tau n) = b(n); n is an element of N in the sublinear (0 < alpha < 1) and the superlinear (1 < alpha) cases are also discussed.
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    Article
    Citation - WoS: 19
    Citation - Scopus: 21
    Lyapunov Type Inequalities for Mixed Nonlinear Riemann-Liouville Fractional Differential Equations With a Forcing Term
    (Elsevier, 2017) Agarwal, Ravi P.; Ozbekler, Abdullah
    In this paper, we present some new Lyapunov and Hartman type inequalities for Riemann-Liouville fractional differential equations of the form ((a)D(alpha)x)(t) + p(t) vertical bar x(t) vertical bar(mu-1) x(t) + q(t) vertical bar x(t) vertical bar(gamma-1) x(t) = f(t), where p, q, f are real-valued functions and 0 < gamma < 1 < mu < 2. No sign restrictions are imposed on the potential functions p, q and the forcing term f. The inequalities obtained generalize and compliment the existing results for the special cases of this equation in the literature. (C) 2016 Elsevier B.V. All rights reserved.
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    Article
    Citation - WoS: 2
    Citation - Scopus: 3
    Lyapunov-Type Inequalities for Lidstone Boundary Value Problems on Time Scales
    (Springer-verlag Italia Srl, 2020) Agarwal, Ravi P.; Oguz, Arzu Denk; Ozbekler, Abdullah; Denk Oğuz, Arzu
    In this paper, we establish new Hartman and Lyapunov-type inequalities for even-order dynamic equations x.2n (t) + (-1)n-1q(t) xs (t) = 0 on time scales T satisfying the Lidstone boundary conditions x.2i (t1) = x.2i (t2) = 0; t1, t2. [t0,8) T for i = 0, 1,..., n - 1. The inequalities obtained generalize and complement the existing results in the literature.
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    Article
    Citation - WoS: 19
    Citation - Scopus: 21
    Interval Criteria for the Forced Oscillation of Super-Half Differential Equations Under Impulse Effects
    (Pergamon-elsevier Science Ltd, 2009) Ozbekler, A.; Zafer, A.
    In this paper, we derive new interval oscillation criteria for a forced super-half-linear impulsive differential equation having fixed moments of impulse actions. The results are extended to a more general class of nonlinear impulsive differential equations. Examples are also given to illustrate the relevance of the results. (C) 2009 Elsevier Ltd. All rights reserved.
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    Article
    Citation - WoS: 3
    Citation - Scopus: 3
    Picone Type Formula for Half-Linear Impulsive Differential Equations With Discontinuous Solutions
    (Wiley-blackwell, 2015) Ozbekler, A.
    Picone type formula for half-linear impulsive differential equations with discontinuous solutions having fixed moments of impulse actions is derived. Employing the formula, Leighton and Sturm-Picone type comparison theorems as well as several oscillation criteria for impulsive differential equations are obtained. Copyright (c) 2014 John Wiley & Sons, Ltd.
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    Book
    Citation - Scopus: 27
    Lyapunov Inequalities and Applications
    (Springer International Publishing, 2021) Agarwal,R.P.; Bohner,M.; Özbekler,A.
    This book provides an extensive survey on Lyapunov-type inequalities. It summarizes and puts order into a vast literature available on the subject, and sketches recent developments in this topic. In an elegant and didactic way, this work presents the concepts underlying Lyapunov-type inequalities, covering how they developed and what kind of problems they address. This survey starts by introducing basic applications of Lyapunov's inequalities. It then advances towards even-order, odd-order, and higher-order boundary value problems; Lyapunov and Hartman-type inequalities; systems of linear, nonlinear, and quasi-linear differential equations; recent developments in Lyapunov-type inequalities; partial differential equations; linear difference equations; and Lyapunov-type inequalities for linear, half-linear, and nonlinear dynamic equations on time scales, as well as linear Hamiltonian dynamic systems. Senior undergraduate students and graduate students of mathematics, engineering, and science will benefit most from this book, as well as researchers in the areas of ordinary differential equations, partial differential equations, difference equations, and dynamic equations. Some background in calculus, ordinary and partial differential equations, and difference equations is recommended for full enjoyment of the content. © Springer Nature Switzerland AG 2021. All rights reserved.