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The main aim of the current paper is to propose a new numerical scheme based on the Adams-Bashforth method for solving two component time fractional differential equations involving the Caputo-Prabhakar fractional derivative of order μ. The existence and uniqueness of the solutions based on the Adams-Bashforth method reported for two component differential equations are discussed. Also, in this paper stability and convergence are demonstrated. Moreover, two numerical example are demonstrated in order to show the validity and reliability of the proposed methods. [ABSTRACT FROM AUTHOR]

In this article, we use the Haar wavelets (HWs) method to numerically solve the nonlinear Drinfel’d–Sokolov (DS) system. For this purpose, we use an approximation of functions with the help of HWs, and we approximate spatial derivatives using this method. In this regard, to linearize the nonlinear terms of the equations, we use the quasilinearization technique. At the end, to show the effectiveness and accuracy of the method in solving this system one numerical example is provided. [ABSTRACT FROM AUTHOR]

In this paper, for the first time, the distributed‐order time‐fractional forced Korteweg–de Vries equation is studied. We use a numerical method based on the shifted Legendre operational matrix of distributed‐order fractional derivative with Tau method to find approximate solution of distributed‐order forced Korteweg–de Vries equation. This shifted Legendre operational matrix of distributed‐order fractional derivative with Tau method is used to reduce the solution of the distributed‐order time‐fractional forced Korteweg–de Vries equations to a system of algebraic equations. An error analysis and convergence are obtained. Finally, to display the applicability and validity of the numerical method, some examples are implemented. [ABSTRACT FROM AUTHOR]

In this paper, we propose a numerical scheme based on the iterative method for solving the fractional diffusion‐wave equation involving the Caputo–Weyl fractional derivative of order 0<α≤2. The convergence of the approximate solutions of the fractional diffusion‐wave equation is rigourously established. Moreover, the approximate solutions of the fractional diffusion‐wave equation have been presented graphically. [ABSTRACT FROM AUTHOR]

In this paper, we use Chebyshev polynomials to seek the numerical solution of a class of multi-variable order fractional differential equation (MVODEs) that the fractional derivative is described in the Caputo-Prabhakar sense. Using operational matrices, the original equations are transferred to a system of algebraic equations. By solving the system of equations, the numerical solutions are acquired that this system may be solved numerically using an iterative algorithm. The effectiveness and convergence analysis of the numerical scheme is illustrated through four numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and analyze a mathematical model of a viral infection with explicit age-since infection structure for infected cells. We extend previous age-structured within-host virus models by including logistic growth of target cells and allowing for absorption of multiple virus particles by infected cells. The persistence of the virus is shown to depend on the basic reproduction number R0. In particular, when R0 ⩽ 1, the infection free equilibrium is globally asymptotically stable, and conversely if R0 > 1, then the infection free equilibrium is unstable, the system is uniformly persistent and there exists a unique positive equilibrium. We show that our system undergoes a Hopf bifurcation through which the infection equilibrium loses the stability and periodic solutions appear. [ABSTRACT FROM AUTHOR]

In this paper, we present a new method for solving a nonlinear third-order Korteweg–de Vries equation. This method is based on the multiquadric (MQ) quasi-interpolation operator L W 2 and an integrated radial basis function networks scheme. In the present scheme, the second-order central divided difference of the spatial derivative is used to approximate the third-order spatial derivative, and the Taylors series expansion to discretize the temporal derivative. Then, the spatial derivative is approximated by the MQ quasi-interpolation operator L W 2 . This method is applied on some test experiments and the numerical results have been compared with the exact solutions and the solutions of other numerical methods. The L ∞ , L 2 and root-mean-square errors of the solutions show the efficiency and the accuracy of the method. Furthermore, the stability analysis of the method is surveyed. [ABSTRACT FROM AUTHOR]