Scopus İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651

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Now showing 1 - 10 of 17
  • Article
    Citation - Scopus: 12
    On Periodic Solutions of Linear Impulsive Delay Differential Systems
    (2008) Alzabut, Jehad; Akhmet, M.U.; Alzabut, J.O.; Zafer, A.; Matematik
    A necessary and sufficient condition is established for the existence of periodic solutions of linear impulsive delay differential systems. Copyright © 2008 Watam Press.
  • Article
    An Exponential Estimate for Solutions of Linear Impulsive Delay Differential Equations
    (Academic Publication Council, 2007) Alzabut, Jehad; Alzabut, Jehad; Abdeljawad, Thabet; Abdeljawad, Thabet; Matematik
    This paper is concerned with linear impulsive delay differential equations with impulsive conditions allowing delays in the index of the jumps. We obtain an exponential estimate for the solutions of such types of equations. In preparation to this, we present three essential lemmas related to the adjoint equation, the representation of solutions and a bound for the fundamental matrix. Moreover, a sharper estimate is provided.
  • Article
    Citation - WoS: 2
    Citation - Scopus: 7
    A 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; Matematik
    Time 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: 10
    Third-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: 11
    Oscillation 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: 8
    First-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).
  • Book Part
    A Stability Criterion for Delay Differential Equations With Impulse Effects
    (World Scientific Publishing Co., 2007) Alzabut, J.O.
    In this paper, we prove that if a delay differential equation with impulse effects of the form x’(t) = A(t)x(t) + B(t)x(t - τ), t ≠ θi, Δx(θi) = Cix(θi) + Dix(θi-j); i ∈ 2 N; verfies a Perron condition then its trivial solution is uniformly asymptotically stable. © 2007 by World Scientific Publishing Co. Pte. Ltd. All rights reserved.
  • Article
    Citation - WoS: 35
    Citation - Scopus: 35
    On Existence of a Globally Attractive Periodic Solution of Impulsive Delay Logarithmic Population Model
    (Elsevier Science inc, 2008) Alzabut, Jehad O.; Abdeljawad, Thabet
    In this paper, it is shown that a logarithmic population model which is governed by impulsive delay differential equation has a globally attractive periodic solution. (c) 2007 Elsevier Inc. All rights reserved.
  • Article
    Citation - WoS: 33
    Citation - Scopus: 40
    Higher Order Fractional Variational Optimal Control Problems With Delayed Arguments
    (Elsevier Science inc, 2012) Jarad, Fahd; Abdeljawad (Maraaba), Thabet; Baleanu, Dumitru; Abdeljawad , Thabet
    This 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: 14
    Citation - Scopus: 18
    Oscillation of Even Order Nonlinear Delay Dynamic Equations on Time Scales
    (Springer Heidelberg, 2013) Mert, Raziye; Peterson, Allan; Zafer, Agacik; Erbe, Lynn
    One 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.