Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 2Citation - Scopus: 7A Necessary and Sufficient Condition for Oscillation of Second Order Sublinear Delay Dynamic Equations(Amer inst Mathematical Sciences-aims, 2011) Mert, RazIye; Mert, Raziye; Zafer, Agacik; MatematikTime scale calculus approach allows one to treat the continuous, discrete, as well as more general systems simultaneously. In this article we use this tool to establish a necessary and sufficient condition for the oscillation of a class of second order sublinear delay dynamic equations on time scales. Some well known results in the literature are improved and extended.Article Citation - Scopus: 11Oscillation Result for Half-Linear Delay Di Erence Equations of Second-Order(American Institute of Mathematical Sciences, 2022) Santra, S.S.; Baleanu, D.; Edwan, R.; Govindan, V.; Murugesan, A.; Altanji, M.; Jayakumar, C.In this paper, we obtain the new single-condition criteria for the oscillation of secondorder half-linear delay difference equation. Even in the linear case, the sharp result is new and, to our knowledge, improves all previous results. Furthermore, our method has the advantage of being simple to prove, as it relies just on sequentially improved monotonicities of a positive solution. Examples are provided to illustrate our results. © 2022 the Author(s), licensee AIMS Press.Article Oscillation criteria for even order dynamic equations on time-scales(Dynamic Publishers, Inc, 2011) Grace, Said R.; Agarwal, Ravi P.; Kaymakçalan, Billur; Baoguo, Jia; Erbe, Lynn; Mert, RaziyeSome new criteria for the oscillation of even order linear dynamic equations on time-scales of the form xΔn(t) + q(t)x(t) = 0 are established.Article Citation - Scopus: 8Odd-Order Differential Equations With Deviating Arguments: Asymptomatic Behavior and Oscillation(American Institute of Mathematical Sciences, 2022) Muhib, A.; Dassios, I.; Baleanu, D.; Santra, S.S.; Moaaz, O.Despite the growing interest in studying the oscillatory behavior of delay differential equations of even-order, odd-order equations have received less attention. In this work, we are interested in studying the oscillatory behavior of two classes of odd-order equations with deviating arguments. We get more than one criterion to check the oscillation in different methods. Our results are an extension and complement to some results published in the literature. © 2022 the Author(s), licensee AIMS Press.Article Citation - Scopus: 2Simplified and Improved Criteria for Oscillation of Delay Differential Equations of Fourth Order(Springer Science and Business Media Deutschland GmbH, 2021) Muhib, A.; Baleanu, D.; Alharbi, W.; Mahmoud, E.E.; Moaaz, O.An interesting point in studying the oscillatory behavior of solutions of delay differential equations is the abbreviation of the conditions that ensure the oscillation of all solutions, especially when studying the noncanonical case. Therefore, this study aims to reduce the oscillation conditions of the fourth-order delay differential equations with a noncanonical operator. Moreover, the approach used gives more accurate results when applied to some special cases, as we explained in the examples. © 2021, The Author(s).Article Citation - Scopus: 8First-Order Impulsive Differential Systems: Sufficient and Necessary Conditions for Oscillatory or Asymptotic Behavior(Springer Science and Business Media Deutschland GmbH, 2021) Baleanu, D.; Khedher, K.M.; Moaaz, O.; Santra, S.S.In this paper, we study the oscillatory and asymptotic behavior of a class of first-order neutral delay impulsive differential systems and establish some new sufficient conditions for oscillation and sufficient and necessary conditions for the asymptotic behavior of the same impulsive differential system. To prove the necessary part of the theorem for asymptotic behavior, we use the Banach fixed point theorem and the Knaster–Tarski fixed point theorem. In the conclusion section, we mention the future scope of this study. Finally, two examples are provided to show the defectiveness and feasibility of the main results. © 2021, The Author(s).Article Citation - Scopus: 40More Effective Criteria for Oscillation of Second-Order Differential Equations With Neutral Arguments(MDPI AG, 2020) Anis, M.; Baleanu, D.; Muhib, A.; Moaaz, O.The motivation for this paper is to create new criteria for oscillation of solutions of second-order nonlinear neutral differential equations. In more than one respect, our results improve several related ones in the literature. As proof of the effectiveness of the new criteria, we offer more than one practical example. © 2020 by the authors.Article Citation - WoS: 7Citation - Scopus: 10Oscillation of Higher-Order Neutral Dynamic Equations on Time Scales(Springeropen, 2012) Mert, RaziyeIn this article, using comparison with second-order dynamic equations, we establish sufficient conditions for oscillatory solutions of an nth-order neutral dynamic equation with distributed deviating arguments. The arguments are based on Taylor monomials on time scales. 2000 Mathematics Subject Classification: 34K11; 39A10; 39A99.Article Citation - WoS: 8Citation - Scopus: 5Oscillatory Behavior of Higher-Order Neutral Type Dynamic Equations(Univ Szeged, Bolyai institute, 2013) Mert, Raziye; Zafer, Agacik; Grace, Said R.The oscillation behavior of solutions for higher-order delay dynamic equations of neutral type is investigated by making use of comparison with second-order dynamice quations. The method can be utilized to study other types of higher-order equations on time scales as well.Article Citation - WoS: 14Citation - Scopus: 18Oscillation of Even Order Nonlinear Delay Dynamic Equations on Time Scales(Springer Heidelberg, 2013) Mert, Raziye; Peterson, Allan; Zafer, Agacik; Erbe, LynnOne of the important methods for studying the oscillation of higher order differential equations is to make a comparison with second order differential equations. The method involves using Taylor's Formula. In this paper we show how such a method can be used for a class of even order delay dynamic equations on time scales via comparison with second order dynamic inequalities. In particular, it is shown that nonexistence of an eventually positive solution of a certain second order delay dynamic inequality is sufficient for oscillation of even order dynamic equations on time scales. The arguments are based on Taylor monomials on time scales.