Özbekler, Abdullah
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Abdullah, Özbekler
A., Ozbekler
Ozbekler, Abdullah
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Abdullah, Ozbekler
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Ozbekler,A.
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Özbekler,A.
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Özbekler, Abdullah
Ozbekler, A.
Oezbekler, A.
A., Ozbekler
Ozbekler, Abdullah
O., Abdullah
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Abdullah, Ozbekler
A.,Ozbekler
Ozbekler,A.
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Özbekler,A.
A.,Özbekler
Özbekler, Abdullah
Ozbekler, A.
Oezbekler, A.
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abdullah.ozbekler@atilim.edu.tr
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Scholarly Output
45
Articles
41
Citation Count
267
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0
38 results
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Now showing 1 - 10 of 38
Article Citation Count: 1Lyapunov type inequalities for second-order differential equations with mixed nonlinearities(Walter de Gruyter GmbH, 2016) Özbekler, Abdullah; Özbekler,A.; MathematicsIn this paper,we present some new Lyapunov and Hartman type inequalities for second-order equations with mixed nonlinearities: x''(t) + p(t)|x(t)|β?1x(t) + q(t)|x(t)|y?1x(t) = 0, where p(t), q(t) are real-valued functions and 0 < γ < 1 < β < 2. No sign restrictions are imposed on the potential functions p(t) and q(t). The inequalities obtained generalize the existing results for the special cases of this equation in the literature. © 2016 by De Gruyter.Article Citation Count: 9On the Oscillation of Non-Linear Fractional Difference Equations with Damping(Mdpi, 2019) Özbekler, Abdullah; Muthulakshmi, Velu; Ozbekler, Abdullah; Adigilzel, Hakan; MathematicsIn studying the Riccati transformation technique, some mathematical inequalities and comparison results, we establish new oscillation criteria for a non-linear fractional difference equation with damping term. Preliminary details including notations, definitions and essential lemmas on discrete fractional calculus are furnished before proceeding to the main results. The consistency of the proposed results is demonstrated by presenting some numerical examples. We end the paper with a concluding remark.Article Citation Count: 6Sturmian theory for second order differential equations with mixed nonlinearities(Elsevier Science inc, 2015) Özbekler, Abdullah; MathematicsIn the paper, Sturmian comparison theory is developed for the pair of second order differential equations; first of which is the nonlinear differential equations (m(t)y')' + s(t)y' + Sigma(n)(i=1)q(i)(t)vertical bar y vertical bar(proportional to j-1)y = 0, with mixed nonlinearities alpha(1) > ... > alpha(m) > 1 > alpha(m+1) > ... > alpha(n), and the second is the non-selfadjoint differential equations (k(t)x')' + r(t)x' + p(t)x = 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. (C) 2015 Elsevier Inc. All rights reserved.Article Citation Count: 0DE LA VALLEE POUSSIN INEQUALITY FOR IMPULSIVE DIFFERENTIAL EQUATIONS(Walter de Gruyter Gmbh, 2021) Akgöl, Sibel Doğru; Özbekler, Abdullah; MathematicsThe 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 SciencesArticle Citation Count: 1Oscillation Results for a Class of Nonlinear Fractional Order Difference Equations with Damping Term(Hindawi Ltd, 2020) Özbekler, Abdullah; Alzabut, Jehad; Jacintha, Mary; Ozbekler, Abdullah; MathematicsThe 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.Article Citation Count: 0On the oscillation of Volterra integral equations with positive and negative nonlinearities(Wiley-blackwell, 2016) Özbekler, Abdullah; MathematicsIn the paper, we give new oscillation criteria for Volterra integral equations having different nonlinearities such as superlinearity and sublinearity. We also present some new sufficient conditions for oscillation under the effect of oscillatory forcing term. Copyright (C) 2015 JohnWiley & Sons, Ltd.Conference Object Citation Count: 3Forced Oscillation of Second-Order Impulsive Differential Equations with Mixed Nonlinearities(Springer, 2013) Özbekler, Abdullah; Zafer, A.; MathematicsIn this paper we give new oscillation criteria for a class of second-order mixed nonlinear impulsive differential equations having fixed moments of impulse actions. The method is based on the existence of a nonprincipal solution of a related second-order linear homogeneous equation.Article Citation Count: 2NEW RESULTS FOR OSCILLATORY PROPERTIES OF NEUTRAL DIFFERENTIAL EQUATIONS WITH A p-LAPLACIAN LIKE OPERATOR(Univ Miskolc inst Math, 2020) Özbekler, Abdullah; Grace, S. R.; Alzabut, J.; Ozbekler, A.; MathematicsResults reported in this paper provide a generalization for some previously obtained results. Based on comparing with the oscillatory behavior of first-order delay equations, we provide new oscillation criteria for the solutions of even-order neutral differential equations with a p-Laplacian like operator. The proposed theorems not only provide totally different approach but also essentially improve a number of results reported in the literature. To demonstrate the advantage of our results, we present two examples.Article Citation Count: 16Forced oscillation of super-half-linear impulsive differential equations(Pergamon-elsevier Science Ltd, 2007) Özbekler, Abdullah; Zafer, A.; MathematicsBy using a Picone type formula in comparison with oscillatory unforced half-linear equations, we derive new oscillation criteria for second order forced super-half-linear impulsive differential equations having fixed moments of impulse actions. In the superlinear case, the effect of a damping term is also considered. (c) 2007 Elsevier Ltd. All rights reserved.Article Citation Count: 15Disconjugacy via Lyapunov and Vallee-Poussin type inequalities for forced differential equations(Elsevier Science inc, 2015) Özbekler, Abdullah; Ozbekler, Abdullah; MathematicsIn the case of oscillatory potentials, we present some new Lyapunov and Vallee-Poussin type inequalities for second order forced differential equations. No sign restriction is imposed on the forcing term. The obtained inequalities generalize and compliment the existing results in the literature. (C) 2015 Elsevier Inc. All rights reserved.
