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
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Mathematics
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Former Staff
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Scholarly Output

42

Articles

39

Views / Downloads

112/0

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0

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0

WoS Citation Count

272

Scopus Citation Count

338

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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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Author: Ozbekler, Abdullah

Scholarly Output Search Results

Now showing 1 - 10 of 25
  • Thumbnail Image
    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
    Sturmian Comparison Theory for Half-Linear and Nonlinear Differential Equations Via Picone Identity
    (Univ Nis, Fac Sci Math, 2017) Ozbekler, Abdullah
    In this paper, Sturmian comparison theory is developed for the pair of second order differential equations; first of which is the nonlinear differential equations of the form (m(t)Phi(beta) (y'))' + Sigma (n) (i = 1) qi(t)Phi(alpha i) (y) = 0 and the second is the half-linear differential equations (k(t)Phi(beta) (x'))' + p(t) Phi(beta) (x) = 0 where Phi(*)(s) = \ s \(*-1)s and alpha(1) > . . .> alpha(m) > beta > alpha(m + 1) > . . . > alpha(n) > 0. Under the assumption that the solution of Eq. (2) has two consecutive zeros, we obtain Sturm-Picone type and Leighton type comparison theorems for Eq. (1) by employing the new nonlinear version of Picone's formula that we derive. Wirtinger type inequalities and several oscillation criteria are also attained for Eq. (1). Examples are given to illustrate the relevance of the results.
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    Article
    Citation - WoS: 1
    Citation - Scopus: 1
    Forced Oscillation of Sublinear Impulsive Differential Equations Via Nonprincipal Solution
    (Wiley, 2018) Mostepha, Naceri; Ozbekler, Abdullah
    In this paper, we give new oscillation criteria for forced sublinear impulsive differential equations of the form (r(t)x')' + q(t)vertical bar x vertical bar(gamma-1) x = f(t), t not equal theta(i); Delta r(t)x' + q(i)vertical bar x vertical bar(gamma-1) x = f(i), t = theta(i), where gamma is an element of(0, 1), under the assumption that associated homogenous linear equation (r(t)z')' + q(t)z = 0, t not equal theta(i); Delta r(t)z' + q(i)z = 0, t = theta(i). is nonoscillatory.
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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: 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: 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: 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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    Article
    Citation - WoS: 1
    Citation - Scopus: 1
    Sub-Linear Oscillations via Nonprincipal Solution
    (Editura Acad Romane, 2018) Ozbekler, Abdullah; Mathematics
    In the paper, we give new oscillation criteria for forced sub-linear differential equations with "oscillatory potentials" under the assumption that corresponding linear homogeneous equation is nonoscillatory.
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    Article
    Citation - WoS: 35
    Citation - Scopus: 44
    Lyapunov-Type Inequalities for Mixed Non-Linear Forced Differential Equations Within Conformable Derivatives
    (Springer, 2018) Abdeljawad, Thabet; Agarwal, Ravi P.; Alzabut, Jehad; Jarad, Fahd; Ozbekler, Abdullah
    We state and prove new generalized Lyapunov-type and Hartman-type inequalities fora conformable boundary value problem of order alpha is an element of (1,2] with mixed non-linearities of the form ((T alpha X)-X-a)(t) + r(1)(t)vertical bar X(t)vertical bar(eta-1) X(t) + r(2)(t)vertical bar x(t)vertical bar(delta-1) X(t) = g(t), t is an element of (a, b), satisfying the Dirichlet boundary conditions x(a) = x(b) = 0, where r(1), r(2), and g are real-valued integrable functions, and the non-linearities satisfy the conditions 0 < eta < 1 < delta < 2. Moreover, Lyapunov-type and Hartman-type inequalities are obtained when the conformable derivative T-alpha(a) is replaced by a sequential conformable derivative T-alpha(a) circle T-alpha(a), alpha is an element of (1/2,1]. The potential functions r(1), r(2) as well as the forcing term g require no sign restrictions. The obtained inequalities generalize some existing results in the literature.