Matematik Bölümü Yayın Koleksiyonu

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

Browse

Filters

20163

Settings

Author: search.filters.author.Alipour, MohsenSubject: search.filters.subject.Caputo Fractional Derivative

Search Results

Now showing 1 - 3 of 3
  • Article
    Citation - WoS: 11
    Numerical and Bifurcations Analysis for Multi Order Fractional Model of Hiv Infection of Cd4+t-cells
    (Univ Politehnica Bucharest, Sci Bull, 2016) Alipour, Mohsen; Baleanu, Dumitru; Arshad, Sadia; Baleanu, Dumitru; Matematik
    In this paper, we solve the dynamical system of HIV infection of CD4(+) T cells within the multi-order fractional derivatives. The Bernstein operational matrices in arbitrary interval [a,b] are applied to obtain the approximate analytical solution of the model. In this way, the fractional differential equations are reduced to an algebraic easily solvable system. The obtained solutions are accurate and the method is very efficient and simple in implementation. With the help of bifurcation analysis, we acquired the critical value of viral death rate, that is, if viral death rate is greater than the critical value then level of virus particles starts to decline and thus free virus will eventually eliminate and patient is cured. Further, we found the threshold for viral infection rate analytically, which assures the stability of uninfected equilibrium and virus will ultimately eradicate.
  • Article
    Numerical and Bifurcations Analysis for Multi Order Fractional Model of Hiv Infection of Cd4(+)T-Cells
    (Univ Politehnica Bucharest, 2016) Alipour, Mohsen; Arshad, Sadia; Baleanu, Dumitru
    In this paper, we solve the dynamical system of HIV infection of CD4(+) T cells within the multi-order fractional derivatives. The Bernstein operational matrices in arbitrary interval [a,b] are applied to obtain the approximate analytical solution of the model. In this way, the fractional differential equations are reduced to an algebraic easily solvable system. The obtained solutions are accurate and the method is very efficient and simple in implementation. With the help of bifurcation analysis, we acquired the critical value of viral death rate, that is, if viral death rate is greater than the critical value then level of virus particles starts to decline and thus free virus will eventually eliminate and patient is cured. Further, we found the threshold for viral infection rate analytically, which assures the stability of uninfected equilibrium and virus will ultimately eradicate.
  • Article
    Citation - WoS: 1
    Citation - Scopus: 1
    On the Kolmogorov Forward Equations Within Caputo and Riemann-Liouville Fractions Derivatives
    (Ovidius Univ Press, 2016) Baleanu, Dumitru; Alipour, Mohsen
    In this work, we focus on the fractional versions of the well-known Kolmogorov forward equations. We consider the problem in two cases. In case 1, we apply the left Caputo fractional derivatives for alpha is an element of (0, 1] and in case 2, we use the right Riemann-Liouville fractional derivatives on R+, for alpha is an element of (1, + infinity). The exact solutions are obtained for the both cases by Laplace transforms and stable subordinators.