Matematik Bölümü Yayın Koleksiyonu

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

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Subject: search.filters.subject.Fractional DerivativeWoS Q: search.filters.wosQuartile.Q4

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Now showing 1 - 4 of 4
  • Article
    Citation - WoS: 7
    On Dynamics of Fractional-Order Model of Hcv Infection
    (Univ Prishtines, 2017) Khodabakhshi, Neda; Baleanu, Dumitru; Vaezpour, S. Mansour; Baleanu, Dumitru; Matematik
    In this paper, we investigate the dynamical behavior of the fractional-order model within Caputo derivative of HCV infection. Stability analysis of the equilibrium points is according to the basic reproduction number R-0. The numerical simulations are also presented to illustrate the results.
  • Article
    Citation - WoS: 8
    Citation - Scopus: 13
    Analysis of Riccati Differential Equations Within a New Fractional Derivative Without Singular Kernel
    (Ios Press, 2017) Lia, Atena; Tejadodi, Haleh; Baleanu, Dumitru; Jafari, Hossein
    Recently Caputo and Fabrizio suggested new definition of fractional derivative that the new kernel has no singularity. In this paper, an analytical method for solving Riccati differential equation with a new fractional derivative is reported. We present numerical results of solving the fractional Riccati differential equations by using the variational iteration method and its modification. The obtained results of two methods demonstrate the efficiency and simplicity of the MVIM that gives good approximations for a larger interval.
  • Article
    Citation - WoS: 3228
    Citation - Scopus: 3356
    New Fractional Derivatives With Non-Local and Non-Singular Kernel Theory and Application To Heat Transfer Model
    (Vinca inst Nuclear Sci, 2016) Baleanu, Dumitru; Atangana, Abdon
    In this paper a new fractional derivative with non-local and no-singular kernel is proposed. Some useful properties of the new derivative are presented and applied to solve the fractional heat transfer model.
  • Article
    Citation - WoS: 147
    Citation - Scopus: 168
    Solving the Fractional Order Bloch Equation
    (Wiley-hindawi, 2009) Feng, Xu; Baleanu, Dumitru; Magin, Richard
    Nuclear magnetic resonance (NMR) is a physical phenomenon widely used in chemistry, medicine, and engineering to study complex materials. NMR is governed by the Bloch equation, which relates a macroscopic model of magnetization to applied radjofrequency, gradient and static magnetic fields. Simple models of materials are well described by the classical first order dynamics of precession and relaxation inherent in the vector form of the Bloch equation. Fractional order generalization of the Bloch equation presents an opportunity to extend its use to describe a wider range of experimental situations involving heterogeneous, porous, or composite materials. Here we describe the generalization of the Bloch equation in terms of Caputo fractional derivatives of order alpha (0 < alpha < 1) for a single spin system in a static magnetic field at resonance. The results are expressed in terms of the Mittag-Leffler function-a generalized exponential function that converges to the classical case when alpha = 1. (C) 2008 Wiley Periodicals, Inc. Concepts Magn Reson Part A 34A: 16-23, 2009.