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

42

Articles

39

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1/0

Supervised MSc Theses

0

Supervised PhD Theses

0

WoS Citation Count

273

Scopus Citation Count

338

WoS h-index

10

Scopus h-index

11

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0

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0

WoS Citations per Publication

6.50

Scopus Citations per Publication

8.05

Open Access Source

15

Supervised Theses

0

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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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Start date: 2007Has files: false

Scholarly Output Search Results

Now showing 1 - 10 of 42
  • Thumbnail Image
    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
    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: 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.
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    Article
    Citation - WoS: 1
    Citation - Scopus: 4
    Second Order Oscillation of Mixed Nonlinear Dynamic Equations With Several Positive and Negative Coefficients
    (Amer inst Mathematical Sciences-aims, 2011) Ozbekler, Abdullah; Zafer, Agacik; Mathematics
    New oscillation criteria are obtained for superlinear and sublinear forced dynamic equations having positive and negative coefficients by means of nonprincipal solutions.
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    Article
    Citation - WoS: 16
    Citation - Scopus: 16
    Lyapunov Type Inequalities for Even Order Differential Equations With Mixed Nonlinearities
    (Springeropen, 2015) Agarwal, Ravi P.; Ozbekler, Abdullah
    In the case of oscillatory potentials, we present Lyapunov and Hartman type inequalities for even order differential equations with mixed nonlinearities: x((2n))(t) + (-1)(n-1) Sigma(m)(i=1) q(i)(t)vertical bar x(t)vertical bar(alpha i-1) x(t) = 0, where n,m epsilon N and the nonlinearities satisfy 0 < alpha(1) < center dot center dot center dot < alpha(j) < 1 < alpha(j+1) < center dot center dot center dot < alpha(m) < 2.
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    Article
    Citation - WoS: 9
    Citation - Scopus: 9
    Nonoscillation and Oscillation of Second-Order Impulsive Differential Equations With Periodic Coefficients
    (Pergamon-elsevier Science Ltd, 2012) Ozbekler, A.; Zafer, A.
    In this paper, we give a nonoscillation criterion for half-linear equations with periodic coefficients under fixed moments of impulse actions. The method is based on the existence of positive solutions of the related Riccati equation and a recently obtained comparison principle. In the special case when the equation becomes impulsive Hill equation new oscillation criteria are also obtained. (C) 2011 Elsevier Ltd. All rights reserved.
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    Article
    Citation - WoS: 2
    Citation - Scopus: 4
    A Sturm Comparison Criterion for Impulsive Hyperbolic Equations
    (Springer-verlag Italia Srl, 2020) Ozbekler, Abdullah; Isler, Kubra Uslu
    In this paper, we investigate the Sturmian comparison theory for hyperbolic equations with fixed moments of effects. The results obtained extend the results of those existing in the literature for Sturmian comparison theory on ordinary and impulsive differential equations to impulsive hyperbolic equations.
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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: 5
    Citation - Scopus: 5
    Oscillation Criteria for Non-Canonical Second-Order Nonlinear Delay Difference Equations With a Superlinear Neutral Term
    (Texas State Univ, 2023) Vidhyaa, Kumar S.; Thandapani, Ethiraju; Alzabut, Jehad; Ozbekler, Abdullah
    We obtain oscillation conditions for non-canonical second-order nonlinear delay difference equations with a superlinear neutral term. To cope with non-canonical types of equations, we propose new oscillation criteria for the main equation when the neutral coefficient does not satisfy any of the conditions that call it to either converge to 0 or & INFIN;. Our approach differs from others in that we first turn into the non-canonical equation to a canonical form and as a result, we only require one condition to weed out non-oscillatory solutions in order to induce oscillation. The conclusions made here are new and have been condensed significantly from those found in the literature. For the sake of confirmation, we provide examples that cannot be included in earlier works.