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.
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Profesör Doktor
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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

272

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

6.48

Scopus Citations per Publication

8.05

Open Access Source

15

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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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Scholarly Output Search Results

Now showing 1 - 10 of 11
  • Thumbnail Image
    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.
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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: 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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    Book Part
    De La Vallée Poussin-type inequality for impulsive dynamic equations on time scales
    (De Gruyter, 2023) Akgöl,S.D.; Özbekler,A.
    We derive a de La Vallée Poussin-type inequality for impulsive dynamic equations on time scales. This inequality is often used in conjunction with disconjugacy and/or (non)oscillation. Hence, it appears to be a very useful tool for the qualitative study of dynamic equations. In this work, generalizing the classical de La Vallée Poussin inequality for impulsive dynamic equations on arbitrary time scales, we obtain a dis-conjugacy criterion and some results on nonoscillation. We also present illustrative examples that support our findings. © 2023 Walter de Gruyter GmbH, Berlin/Bostonl. All rights reserved.
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    Article
    Citation - WoS: 1
    Citation - Scopus: 2
    Oscillation Results for a Class of Nonlinear Fractional Order Difference Equations with Damping Term
    (Hindawi Ltd, 2020) Selvam, A. George Maria; Alzabut, Jehad; Jacintha, Mary; Ozbekler, Abdullah
    The paper studies the oscillation of a class of nonlinear fractional order difference equations with damping term of the form Delta[psi(lambda)z(eta) (lambda)] + p(lambda)z(eta) (lambda) + q(lambda)F(Sigma(lambda-1+mu)(s=lambda 0) (lambda - s - 1)((-mu)) y(s)) = , where z(lambda) = a(lambda) + b(lambda)Delta(mu) y(lambda), Delta(mu) stands for the fractional difference operator in Riemann-Liouville settings and of order mu, 0 < mu <= 1, and eta >= 1 is a quotient of odd positive integers and lambda is an element of N lambda 0+1-mu. New oscillation results are established by the help of certain inequalities, features of fractional operators, and the generalized Riccati technique. We verify the theoretical outcomes by presenting two numerical examples.
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    Article
    Citation - WoS: 4
    New Criteria on Oscillatory and Asymptotic Behavior of Third-Order Nonlinear Dynamic Equations With Nonlinear Neutral Terms
    (Mdpi, 2021) Grace, Said R.; Alzabut, Jehad; Ozbekler, Abdullah
    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
    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: 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 - WoS: 2
    Citation - Scopus: 3
    Lyapunov and Hartman-Type Inequalities for Higher-Order Discrete Fractional Boundary Value Problems
    (Univ Miskolc inst Math, 2023) Oguz, Arzu Denk; Alzabut, Jehad; Ozbekler, Abdullah; Jonnalagadda, Jagan Mohan
    By employing Green's function, we obtain new Lyapunov and Hartman-type inequalities for higher-order discrete fractional boundary value problems. Reported results essentially generalize some theorems existing in the literature. As an application, we discuss the corresponding eigenvalue problems.
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    Article
    Citation - Scopus: 3
    De La Vallee Poussin Inequality for Impulsive Differential Equations
    (Walter de Gruyter Gmbh, 2021) Akgol, Sibel Dogru; Ozbekler, Abdullah
    The de la Vallee Poussin inequality is a handy tool for the investigation of disconjugacy, and hence, for the oscillation/nonoscillation of differential equations. The results in this paper are extensions of former those of Hartman and Wintner [Quart. Appl. Math. 13 (1955), 330-332] to the impulsive differential equations. Although the inequality first appeared in such an early date for ordinary differential equations, its improved version for differential equations under impulse effect never has been occurred in the literature. In the present study, first, we state and prove a de la Vallee Poussin inequality for impulsive differential equations, then we give some corollaries on disconjugacy. We also mention some open problems and finally, present some examples that support our findings. (C) 2021 Mathematical Institute Slovak Academy of Sciences