Fractional-order mathematical modeling and analysis of HIV/AIDS with control strategies incorporating three operators

HIV/AIDS remains a major global public health challenge, necessitating the development of accurate mathematical models to better understand and control its transmission dynamics. In this study, a fractional-order HIV/AIDS model is developed using the Caputo, Caputo–Fabrizio, and Atangana–Baleanu derivatives to capture memory effects and long-term dependencies associated with disease progression. The existence and uniqueness of the model solutions are established through fixed-point theory, thereby ensuring the mathematical well-posedness of the system. Numerical simulations indicate that increasing the fractional order slows the progression and spread of HIV, whereas effective treatment strategies substantially reduce the prevalence of infection and the rate of disease transmission. These findings demonstrate that fractional-order models provide a more realistic representation of epidemic dynamics by accounting for delays and persistence effects. Furthermore, the study underscores the importance of early intervention and sustained treatment coverage in controlling HIV transmission and provides valuable insights for public health policy formulation and resource allocation.