The computational solutions for the fractional mathematical system form of the HIV-1 infection of CD4+ T-cells are investigated by employing three recent analytical schemes along the Atangana–Baleanu fractional (ABF) derivative. This model is affected by antiviral drug therapy, making it an accurate mathematical model to predict the evolution of dynamic population systems involving virus particles. The modified Khater (MKhat), sech–tanh expansion (STE), extended simplest equation (ESE) methods are handled the fractional system and obtained many novel solutions. The Hamiltonian system’s characterizations are used to investigate the stability property of the obtained solutions. Additionally, the solutions are sketched in two-dimensional to demonstrate a visual representation of the relationship between variables.