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 12
  • 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 - 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.
  • Article
    Citation - WoS: 35
    Citation - Scopus: 44
    Generalized Fractional Order Bloch Equation With Extended Delay
    (World Scientific Publ Co Pte Ltd, 2012) Daftardar-Gejji, Varsha; Baleanu, Dumitru; Magin, Richard; Bhalekar, Sachin
    The fundamental description of relaxation (T-1 and T-2) in nuclear magnetic resonance (NMR) is provided by the Bloch equation, an integer-order ordinary differential equation that interrelates precession of magnetization with time-and space-dependent relaxation. In this paper, we propose a fractional order Bloch equation that includes an extended model of time delays. The fractional time derivative embeds in the Bloch equation a fading power law form of system memory while the time delay averages the present value of magnetization with an earlier one. The analysis shows different patterns in the stability behavior for T-1 and T-2 relaxation. The T-1 decay is stable for the range of delays tested (1 mu sec to 200 mu sec), while the T-2 relaxation in this extended model exhibits a critical delay (typically 100 mu sec to 200 mu sec) above which the system is unstable. Delays arise in NMR in both the system model and in the signal excitation and detection processes. Therefore, by adding extended time delay to the fractional derivative model for the Bloch equation, we believe that we can develop a more appropriate model for NMR resonance and relaxation.
  • Article
    Citation - WoS: 108
    Citation - Scopus: 123
    Fractional Bloch Equation With Delay
    (Pergamon-elsevier Science Ltd, 2011) Daftardar-Gejji, Varsha; Baleanu, Dumitru; Magin, Richard; Bhalekar, Sachin
    In 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: 41
    Citation - Scopus: 46
    Fractional Variational Principles With Delay Within Caputo Derivatives
    (Pergamon-elsevier Science Ltd, 2010) Jarad, Fahd; Abdeljawad (Maraaba), Thabet; Baleanu, Dumitru; Abdeljawad , Thabet
    In this paper we investigate the fractional variational principles within Caputo derivatives in the presence of delay derivatives. The corresponding Euler-Lagrange equations are obtained for the case of one dependent variable. A generalization to it dependent variables is obtained. Physical example is analyzed in detail.
  • Article
    Citation - WoS: 48
    Citation - Scopus: 57
    Fractional Variational Optimal Control Problems With Delayed Arguments
    (Springer, 2010) Jarad, Fahd; Abdeljawad, Thabet; Baleanu, Dumitru
    The paper deals with optimal control problems in the presence of delay in the state variables as well as the presence of the Riemann-Liouville fractional derivatives of the state variables. One example is analyzed in detail.
  • Article
    Citation - WoS: 74
    Citation - Scopus: 86
    On the Existence and the Uniqueness Theorem for Fractional Differential Equations With Bounded Delay Within Caputo Derivatives
    (Science Press, 2008) Abdeljawad, Thabet; Jarad, Fahd; Baleanu, Dumitru; Maraaba, Thabet Abdeljawad
    Local and global existence and uniqueness theorems for a functional delay fractional differential equation with bounded delay are investigated. The continuity with respect to the initial function is proved under Lipschitz and the continuity kind conditions are analyzed.