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In this manuscript, an HIV/AIDS epidemic model including five compartments of and is proposed under fractal-fractional-order derivative. The existence theory utilizing Schaefer- and Banach-type fixed point theorems for the solution of considered model is constructed. Additionally, Ulam–Hyers and generalized stability conditions via nonlinear functional analysis are established. A fractional type of two-step Lagrange polynomial known as fractional Adams–Bashforth (AB) method is developed for numerical simulation of the considered model. The simulated results for various fractal-fractional orders are tested on some existing real data of disease spread in South Africa and show that the values of are decreased after treatment was started. In addition, , the population of infected people who have changed their sexual habits sufficiently after starting the treatment and changing their …