Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - Scopus: 10Third-Order Neutral Differential Equations of the Mixed Type: Oscillatory and Asymptotic Behavior(American Institute of Mathematical Sciences, 2022) Qaraad, B.; Moaaz, O.; Baleanu, D.; Santra, S.S.; Ali, R.; Elabbasy, E.M.In this work, by using both the comparison technique with first-order differential inequalities and the Riccati transformation, we extend this development to a class of third-order neutral differential equations of the mixed type. We present new criteria for oscillation of all solutions, which improve and extend some existing ones in the literature. In addition, we provide an example to illustrate our results. © 2022 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)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 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 - WoS: 33Citation - Scopus: 40Higher Order Fractional Variational Optimal Control Problems With Delayed Arguments(Elsevier Science inc, 2012) Jarad, Fahd; Abdeljawad (Maraaba), Thabet; Baleanu, Dumitru; Abdeljawad , ThabetThis article deals with higher order Caputo fractional variational problems in the presence of delay in the state variables and their integer higher order derivatives. (C) 2012 Elsevier Inc. All rights reserved.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.Article Citation - WoS: 108Citation - Scopus: 123Fractional Bloch Equation With Delay(Pergamon-elsevier Science Ltd, 2011) Daftardar-Gejji, Varsha; Baleanu, Dumitru; Magin, Richard; Bhalekar, SachinIn this paper we investigate a fractional generalization of the Bloch equation that includes both fractional derivatives and time delays. The appearance of the fractional derivative on the left side of the Bloch equation encodes a degree of system memory in the dynamic model for magnetization. The introduction of a time delay on the right side of the equation balances the equation by also adding a degree of system memory on the right side of the equation. The analysis of this system shows different stability behavior for the T-1 and the T-2 relaxation processes. The T-1 decay is stable for the range of delays tested (1-100 mu s), while the T-2 relaxation in this model exhibited a critical delay (typically 6 mu s) above which the system was unstable. Delays are expected to appear in NMR systems, in both the system model and in the signal excitation and detection processes. Therefore, by including both the fractional derivative and finite time delays in the Bloch equation, we believe that we have established a more complete and more realistic model for NMR resonance and relaxation. (C) 2011 Elsevier Ltd. All rights reserved.Article Citation - WoS: 15Citation - Scopus: 16Periodic Solutions, Global Attractivity and Oscillation of an Impulsive Delay Host-Macroparasite Model(Pergamon-elsevier Science Ltd, 2007) Alzabut, J. O.; Saker, S. H.In this paper we will consider the nonlinear impulsive delay host-macroparasite model with periodic coefficients. By means of the continuation theorem of coincidence degree, we establish a sufficient condition for the existence of a positive periodic solution M(t) with strictly positive components. Moreover, we establish a sufficient condition for the global attractivity of M(t) and some sufficient conditions for oscillation of all positive solutions about the positive periodic solution M(t). (c) 2006 Elsevier Ltd. All rights reserved.