The dynamic of HIV infection of CD4$^{+}$ T cells is considered as a
fractional order nonlinear ordinary differential equations system.
In this paper using Laplace transform and Adomian decomposition
method the fractional nonlinear system reduces to a linear algebraic
system. By solving the algebraic system, the solutions are
calculated. The numerical solution of illustrative case study shows
that the purposed method is easy implement and accurate.