Here, we use a fractional model to perform an analytical investigation of (HIV-1 infection of CD4+ T-cells). This considered model is analyzed by utilizing a new extended sub-equation method as well as a direct algebraic method. The obtained results demonstrate the influence and superiority of the applied schemes over other analytical methodologies. The series of single solutions with a fractional derived in order achieved with these methods can be classified as trigonometric, hyperbolic, rational, and other basic functions. A comparison of analytical method results is discussed. We also offer some figures showing how exact the solutions are obtained using the two new analytical methods.