Matematik Bölümü Yayın Koleksiyonu

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

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  • Article
    Citation - WoS: 39
    Citation - Scopus: 42
    A Second Order Accurate Approximation for Fractional Derivatives With Singular and Non-Singular Kernel Applied To a Hiv Model
    (Elsevier Science inc, 2020) Baleanu, Dumitru; Arshad, Sadia; Defterli, Ozlem
    In this manuscript we examine the CD4(+) T cells model of HIV infection under the consideration of two different fractional differentiation operators namely Caputo and Caputo-Fabrizio (CF). Moreover, the generalized HIV model is investigated by considering Reverse Transcriptase (RT) inhibitors as a drug treatment for HIV. The threshold values for the stability of the equilibrium point belonging to non-infected case are calculated for both models with and without treatment. For the numerical solutions of the studied model, we construct trapezoidal approximation schemes having second order accuracy for the approximation of fractional operators with singular and non-singular kernel. The stability and convergence of the proposed schemes are analyzed analytically. To illustrate the dynamics given by these two fractional operators, we perform numerical simulations of the HIV model for different biological scenarios with and without drug concentration. The studied biological cases are identified by considering different values of the parameters such as infection rate, growth rate of CD4(+) T cells, clearance rate of virus particles and also the order of the fractional derivative. (C) 2020 Elsevier Inc. All rights reserved.
  • Article
    Citation - WoS: 18
    Citation - Scopus: 21
    A Spectral Collocation Method With Piecewise Trigonometric Basis Functions for Nonlinear Volterra-Fredholm Integral Equations
    (Elsevier Science inc, 2020) Hajipour, Mojtaba; Baleanu, Dumitru; Amiri, Sadegh
    The aim of this paper is to investigate an efficient numerical method based on a novel shifted piecewise cosine basis for solving Volterra-Fredholm integral equations of the second kind. Using operational matrices of integration for the proposed basis functions, this integral equation is transformed into a system of nonlinear algebraic equations. The convergence and error analysis of the proposed method are studied. Some comparative results are provided to verify the efficiency of the presented method. (C) 2019 Elsevier Inc. All rights reserved.
  • Article
    Citation - WoS: 76
    Citation - Scopus: 82
    On Shifted Jacobi Spectral Approximations for Solving Fractional Differential Equations
    (Elsevier Science inc, 2013) Bhrawy, A. H.; Baleanu, D.; Ezz-Eldien, S. S.; Doha, E. H.
    In this paper, a new formula of Caputo fractional-order derivatives of shifted Jacobi polynomials of any degree in terms of shifted Jacobi polynomials themselves is proved. We discuss a direct solution technique for linear multi-order fractional differential equations (FDEs) subject to nonhomogeneous initial conditions using a shifted Jacobi tau approximation. A quadrature shifted Jacobi tau (Q-SJT) approximation is introduced for the solution of linear multi-order FDEs with variable coefficients. We also propose a shifted Jacobi collocation technique for solving nonlinear multi-order fractional initial value. problems. The advantages of using the proposed techniques are discussed and we compare them with other existing methods. We investigate some illustrative examples of FDEs including linear and nonlinear terms. We demonstrate the high accuracy and the efficiency of the proposed techniques. (C) 2013 Elsevier Inc. All rights reserved.
  • Article
    Citation - WoS: 12
    Citation - Scopus: 12
    A Kamenev-Type Oscillation Result for a Linear (1+α)-Order Fractional Differential Equation
    (Elsevier Science inc, 2015) Mustafa, Octavian G.; O'Regan, Donal; Baleanu, Dumitru; Bəleanu, Dumitru
    We investigate the eventual sign changing for the solutions of the linear equation (x((alpha)))' + q(t)x = t >= 0, when the functional coefficient q satisfies the Kamenev-type restriction lim sup 1/t epsilon integral(t)(to) (t - s)epsilon q(s)ds = +infinity for some epsilon > 2; t(0) > 0. The operator x((alpha)) is the Caputo differential operator and alpha is an element of (0, 1). (C) 2015 Elsevier Inc. All rights reserved.
  • Article
    Citation - WoS: 30
    Citation - Scopus: 46
    On Non-Homogeneous Singular Systems of Fractional Nabla Difference Equations
    (Elsevier Science inc, 2014) Baleanu, Dumitru I.; Kalogeropoulos, Grigoris I.; Dassios, Ioannis K.
    In this article we study the initial value problem of a class of non-homogeneous singular systems of fractional nabla difference equations whose coefficients are constant matrices. By taking into consideration the cases that the matrices are square with the leading coefficient singular, non-square and square with a matrix pencil which has an identically zero determinant, we provide necessary and sufficient conditions for the existence and uniqueness of solutions. More analytically we study the conditions under which the system has unique, infinite and no solutions. Furthermore, we provide a formula for the case of the unique solution. Finally, numerical examples are given to justify our theory. Crown Copyright (C) 2013 Published by Elsevier Inc. All rights reserved.
  • 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: 3
    Citation - Scopus: 3
    Third Order Differential Equations With Fixed Critical Points
    (Elsevier Science inc, 2009) Jarad, Fahd; Kessi, Arezki; Mugan, Ugurhan; Adjabi, Yasin; Jrad, Fahd
    The singular point analysis of third order ordinary differential equations which are algebraic in y and y' is presented. Some new third order ordinary differential equations that pass the Painleve test as well as the known ones are found. (C) 2008 Elsevier Inc. All rights reserved.
  • Article
    Citation - WoS: 76
    Citation - Scopus: 85
    Positivity-Preserving Sixth-Order Implicit Finite Difference Weighted Essentially Non-Oscillatory Scheme for the Nonlinear Heat Equation
    (Elsevier Science inc, 2018) Jajarmi, Amin; Malek, Alaeddin; Baleanu, Dumitru; Hajipour, Mojtaba
    This paper presents a class of semi-implicit finite difference weighted essentially non-oscillatory (WENO) schemes for solving the nonlinear heat equation. For the discretization of second-order spatial derivatives, a sixth-order modified WENO scheme is directly implemented. This scheme preserves the positivity principle and rejects spurious oscillations close to non-smooth points. In order to admit large time steps, a class of implicit Runge-Kutta methods is used for the temporal discretization. The implicit parts of these methods are linearized in time by using the local Taylor expansion of the flux. The stability analysis of the semi-implicit WENO scheme with 3-stages form is provided. Finally, some comparative results for one-, two-and three-dimensional PDEs are included to illustrate the effectiveness of the proposed approach. (c) 2017 Elsevier Inc. All rights reserved.
  • Article
    Citation - WoS: 82
    Citation - Scopus: 85
    Fractional Differential Equations of Caputo-Katugampola Type and Numerical Solutions
    (Elsevier Science inc, 2017) Baleanu, Dumitru; Bai, Yunru; Wu, Guocheng; Zeng, Shengda
    This paper is concerned with a numerical method for solving generalized fractional differential equation of Caputo-Katugampola derivative. A corresponding discretization technique is proposed. Numerical solutions are obtained and convergence of numerical formulae is discussed. The convergence speed arrives at O(Delta T1-alpha). Numerical examples are given to test the accuracy. (C) 2017 Elsevier Inc. All rights reserved.
  • Article
    Citation - WoS: 62
    Citation - Scopus: 80
    A New Iterative Technique for a Fractional Model of Nonlinear Zakharov-Kuznetsov Equations Via Sumudu Transform
    (Elsevier Science inc, 2018) Kumar, Manoj; Baleanu, Dumitru; Prakash, Amit
    The main objective of this paper is to suggest a new computational technique namely new iterative Sumudu transform method (NISTM) to solve numerically nonlinear time-fractional Zakharov-Kuznetsov (FZK) equation in two dimensions. We implemented the proposed technique on two test examples, plotted the solution and compared the absolute error with the variational iterative technique (VIM) and homotopy perturbation transform method (HPTM). (C) 2018 Elsevier Inc. All rights reserved.