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Özbekler, Abdullah
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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.
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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abdullah.ozbekler@atilim.edu.tr
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Scholarly Output
45
Articles
41
Citation Count
267
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0
45 results
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Now showing 1 - 10 of 45
Book Part Citation Count: 0De La Vallée Poussin-type inequality for impulsive dynamic equations on time scales(De Gruyter, 2023) Akgöl, Sibel Doğru; Özbekler, Abdullah; MathematicsWe 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.Article Citation Count: 2Lyapunov type inequalities for second-order forced dynamic equations with mixed nonlinearities on time scales(Springer-verlag Italia Srl, 2017) Özbekler, Abdullah; Cetin, Erbil; Ozbekler, Abdullah; MathematicsIn this paper, we present some newHartman and Lyapunov inequalities for second-order forced dynamic equations on time scales T with mixed nonlinearities: x(Delta Delta)(t) + Sigma(n)(k=1) qk (t)vertical bar x(sigma) (t)vertical bar (alpha k-1) x(sigma) (t) = f (t); t is an element of [t(0), infinity)(T), where the nonlinearities satisfy 0 < alpha(1) < ... < alpha(m) < 1 < alpha(m+1) < ... < alpha(n) < 2. No sign restrictions are imposed on the potentials qk, k = 1, 2, ... , n, and the forcing term f. The inequalities obtained generalize and compliment the existing results for the special cases of this equation in the literature.Book Citation Count: 19Lyapunov Inequalities and Applications(Springer International Publishing, 2021) Özbekler, Abdullah; Bohner,M.; Özbekler,A.; MathematicsThis 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.Article Citation Count: 2Wong’s Oscillation Theorem for the Second-Order Delay Differential Equations(Springer New York LLC, 2017) Özbekler, Abdullah; Zafer,A.; Mathematics[No abstract available]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: 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: 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: 4On 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; Özbekler, Abdullah; Mathematics; MathematicsThe 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.Article Citation Count: 0Forced Oscillation of Delay Difference Equations Via Nonprincipal Solution(Wiley, 2018) Ozbekler, Abdullah; Özbekler, Abdullah; MathematicsIn 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.Article Citation Count: 15Lyapunov Type Inequalities for Even Order Differential Equations With Mixed Nonlinearities(Springeropen, 2015) Agarwal, Ravi P.; Özbekler, Abdullah; Ozbekler, Abdullah; MathematicsIn 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.