WoS İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653

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Scopus Q: search.filters.scopusQuartile.Q3Subject: search.filters.subject.Caputo Fractional Derivative

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Now showing 1 - 7 of 7
  • 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
    Citation - WoS: 52
    Citation - Scopus: 54
    Fractional Caputo Heat Equation Within the Double Laplace Transform
    (Editura Acad Romane, 2013) Jarad, Fahd; Anwar, A. M. O.; Jarad, Fahd; Baleanu, Dumitru; Baleanu, D.; Ayaz, F.; Matematik
    The heat equation and its fractional generalization are used in various applications in science and engineering. In this paper firstly we introduce the double Laplace transform of the partial fractional integrals and derivatives which can be used to solve partial differential equations with Caputo fractional derivatives. Secondly, the fractional heat equation was investigated in details with the help of this new generalized transform
  • Article
    Citation - WoS: 6
    Citation - Scopus: 8
    The Role of Obesity in Fractional Order Tumor-Immune Model
    (Univ Politehnica Bucharest, Sci Bull, 2020) Arshad, Sadia; Baleanu, Dumitru; Yildiz, Tugba Akman; Baleanu, Dumitru; Tang, Yifa; Matematik
    This work investigates the tumor-obesity model via a fractional operator to analyze the interactions between cancer and obesity, since fractional derivatives capture the long formation of cancerous tumor cells that might takes years to develop. It is known that fat cells enhance the development of cancerous tumor cells. To examine how the immune system is influenced due to fat cells, interactions of four types of cell population, namely tumor cells, immune cells, normal cells and fat cells are examined. We investigate the equilibrium points and discuss their stability analytically. Numerical simulations are carried out to verify the analytical results, demonstrating that a low fat diet results in a smaller tumor burden as compared to a high-caloric diet.
  • Article
    Citation - WoS: 11
    Citation - Scopus: 14
    Numerical and Bifurcations Analysis for Multi Order Fractional Model of Hiv Infection of Cd4<sup>+</Sup>t-cells
    (Univ Politehnica Bucharest, Sci Bull, 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: 40
    Citation - Scopus: 41
    Numerical Treatment of Time-Fractional Klein-Gordon Equation Using Redefined Extended Cubic B-Spline Functions
    (Frontiers Media Sa, 2020) Abbas, Muhammad; Iqbal, Muhammad Kashif; Baleanu, Dumitru; Amin, Muhammad
    In this article we develop a numerical algorithm based on redefined extended cubic B-spline functions to explore the approximate solution of the time-fractional Klein-Gordon equation. The proposed technique employs the finite difference formulation to discretize the Caputo fractional time derivative of order alpha is an element of (1, 2] and uses redefined extended cubic B-spline functions to interpolate the solution curve over a spatial grid. A stability analysis of the scheme is conducted, which confirms that the errors do not amplify during execution of the numerical procedure. The derivation of a uniform convergence result reveals that the scheme isO(h(2)+ Delta t(2-alpha)) accurate. Some computational experiments are carried out to verify the theoretical results. Numerical simulations comparing the proposed method with existing techniques demonstrate that our scheme yields superior outcomes.
  • 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.
  • Conference Object
    Citation - WoS: 40
    Citation - Scopus: 36
    Solving the Time-Fractional Diffusion Equation Using a Lie Group Integrator
    (Vinca inst Nuclear Sci, 2015) Baleanu, Dumitru; Parto-Haghighi, Mohammad; Darvishi, Elham; Hashemi, Mir Sajjad
    In this paper, we propose a numerical method to approximate the solutions of time fractional diffusion equation which is in the class of Lie group integrators. Our utilized method, namely fictitious time integration method transforms the unknown dependent variable to a new variable with one dimension more. Then the group preserving scheme is used to integrate the new fractional partial differential equations in the augmented space R3+1. Effectiveness and validity of method demonstrated using two examples.