Chaotic behavior of fractional HIV-1 model involving AIDS related cancer cells.

AIDS-related cancers are a major complication in HIV-infected individuals, driven by chronic immune suppression and viral oncogenesis. To better understand the dynamic interplay among healthy cells, HIV-infected cells, and cancer cells, this study proposes a fractional-order HIV-1 model using the Caputo-Fabrizio derivative. The research problem centers on how fractional-order dynamics-representing memory effects-influence the stability and long-term behavior of this biological system, particularly the conditions under which cancer persists alongside HIV infection. The model’s well-posedness is established by proving the existence and uniqueness of solutions, and local stability of equilibria is analyzed, with biological interpretation of the disease-free and coexistence steady states. Notably, numerical simulations employing the three-step fractional Adams-Bashforth method reveal that the system exhibits chaotic dynamics as the fractional order decreases from 1, indicating heightened sensitivity and complex interactions among cell populations. Two- and three-dimensional phase portraits together with time-series analyses demonstrate that lower fractional orders intensify chaotic behavior, suggesting that memory effects critically modulate disease progression and cancer development in HIV-1. These findings underscore the importance of fractional modeling in capturing realistic, biologically plausible dynamics in viral oncogenesis.