Matematik Bölümü Yayın Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413

Browse

Filters

2007 - 200922010 - 20112

Settings

Publisher: search.filters.publisher.Pergamon-elsevier Science LtdSubject: search.filters.subject.Delay

Search Results

Now showing 1 - 4 of 4
  • 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: 28
    Citation - Scopus: 33
    Existence of Periodic Solutions, Global Attractivity and Oscillation of Impulsive Delay Population Model
    (Pergamon-elsevier Science Ltd, 2007) Alzabut, J. O.; Saker, S. H.
    In this paper we consider the nonlinear impulsive delay population model. The main objective is to systematically study the qualitative behavior of the model including existence of periodic solutions, global attractivity and oscillation. The main oscillation results are the results of the prevalence of the mature cells about the periodic solutions and the global attractivity results are the conditions for nonexistence of dynamical diseases on the population. (c) 2006 Elsevier Ltd. All rights reserved.
  • Article
    Citation - WoS: 15
    Citation - Scopus: 16
    Periodic 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.