A. A. M. Arafa

Exact Solutions of Fractional-Order Biological Population Model

In this paper, the Adomians decomposition method (ADM) is presented for finding the exact solutions of a more general biological population models. A new solution is constructed in power series. The fractional derivatives are described in the Caputo sense. To illustrate the reliability of the method, some examples are provided.

Fractional modeling dynamics of HIV and CD4 + T-cells during primary infection

In this paper, we introduce fractional-order into a model of HIV-1 infection of CD4+ T cells. We study the effect of the changing the average number of viral particles N with different sets of initial conditions on the dynamics of the presented model. Generalized Euler method (GEM) will be used to find a numerical solution of the HIV-1 infection fractional order model.

Homotopy Analysis Method for Solving Biological Population Model

In this paper, the homotopy analysis method (HAM) is applied to solve generalized biological population models. The fractional derivatives are described by Caputos sense. The method introduces a significant improvement in this field over existing techniques. Results obtained using the scheme presented here agree well with the analytical solutions and the numerical results presented in Ref. [6]. However, the fundamental solutions of these equations still exhibit useful scaling properties that make them attractive for applications.

New Method for Solving Linear Fractional Differential Equations

We develop a new application of the Mittag-Leffler Function method that will extend the application of the method to linear differential equations with fractional order. A new solution is constructed in power series. The fractional derivatives are described in the Caputo sense. To illustrate the reliability of the method, some examples are provided. The results reveal that the technique introduced here is very effective and convenient for solving linear differential equations of fractional order.

Numerical solutions for some generalized coupled nonlinear evolution equations

Abstract In this paper, the Adomian decomposition method (ADM) is presented for the numerical solutions of the coupled evolution equations of fractional order. The ADM in applied mathematics can be used as an alternative method for obtaining analytic and approximate solutions for different types of fractional differential equations. The fractional derivatives are described in the Caputo sense. The given solutions are compared with the traveling wave solutions. The results obtained are then graphically represented. Finally, numerical results demonstrate the accuracy, efficiency and high rate of convergence of this method.