An analytic study of the fractional order model of HIV-1 virus and CD4+ T-cells using adomian method

In this article, we study the fractional mathematical model of HIV-1 infection of CD4+ T-cells, by studying a system of fractional differential equations of first order with some initial conditions, we study the changing effect of many parameters. The fractional derivative is described in the caputo sense. The adomian decomposition method (Shortly, ADM) method was used to calculate an approximate solution for the system under study. The nonlinear term is dealt with the help of adomian polynomials. Numerical results are presented with graphical justifications to show the accuracy of the proposed methods

An algorithm for positive solution of boundary value problems of nonlinear fractional differential equations by Adomian decomposition method

In this paper, an algorithm based on a new modification, developed by Duan and Rach, for the Adomian decomposition method (ADM) is generalized to find positive solutions for boundary value problems involving nonlinear fractional ordinary differential equations. In the proposed algorithm the boundary conditions are used to convert the nonlinear fractional differential equations to an equivalent integral equation and then a recursion scheme is used to obtain the analytical solution components without the use of undetermined coefficients. Hence, there is no requirement to solve a nonlinear equation or a system of nonlinear equations of undetermined coefficients at each stage of approximation solution as per in the standard ADM. The fractional derivative is described in the Caputo sense. Numerical examples are provided to demonstrate the feasibility of the proposed algorithm

Series solution of the time-dependent Schr\"{o}dinger-Newton equations in the presence of dark energy via the Adomian Decomposition Method

The Schr\"{o}dinger-Newton model is a nonlinear system obtained by coupling the linear Schr\"{o}dinger equation of canonical quantum mechanics with the Poisson equation of Newtonian mechanics. In this paper we investigate the effects of dark energy on the time-dependent Schr\"{o}dinger-Newton equations by including a new source term with energy density $\rho_{\Lambda} = \Lambda c^2/(8\pi G)$, where $\Lambda$ is the cosmological constant, in addition to the particle-mass source term $\rho_m = m|\psi|^2$. The resulting Schr\"{o}dinger-Newton-$\Lambda$ (S-N-$\Lambda$) system cannot be solved exactly, in closed form, and one must resort to either numerical or semianalytical (i.e., series) solution methods. We apply the Adomian Decomposition Method, a very powerful method for solving a large class of nonlinear ordinary and partial differential equations, to obtain accurate series solutions of the S-N-$\Lambda$ system, for the first time. The dark energy dominated regime is also investigated in detail. We then compare our results to existing numerical solutions and analytical estimates, and show that they are consistent with previous findings. Finally, we outline the advantages of using the Adomian Decomposition Method, which allows accurate solutions of the S-N-$\Lambda$ system to be obtained quickly, even with minimal computational resources.Comment: 20 pages, 1 table, 8 figure