A nonlinear fractional order mathematical framework that estimates the concentration of healthy CD4+T cells, concentration of CD4+T cells contaminated by HIV virus, and concentration of free contagious virus particles is solved using a variational iteration method. Iterative analysis has been used to analyse a nonlinear fractional order mathematical model of differential equations. The Caputo derivative has been employed to describe fractional derivatives. By specifying fixed components with different spans of time and computing an infinite series solution for various orders of the system of fractional differential equations. Additionally, the results from the variational iteration method for integer orders are associated with the results from the same technique for various fractional orders. Python is used for analysing the solution numerically and graphically.