This study develops a novel fractional-order HIV infection model capturing the interactions among uninfected and infected \(\hbox {CD4}^+\) T-cells, free HIV particles, and cytotoxic T lymphocyte (CTL) immune responses. The model is formulated within the Caputo fractional derivative framework to account for memory effects, and its fundamental properties—nonnegativity, boundedness, and the existence and uniqueness of solutions—are rigorously established. Equilibrium points and the basic reproduction number ( \(\mathcal {R}_0\) ) are derived, with local and global stability analyses performed. Sensitivity analysis identifies parameters exerting the most significant influence on \(\mathcal {R}_0\) . Two optimal control strategies are incorporated: one enhancing drug efficacy to prevent new infections and the other reducing viral production. The optimal control problem is solved using the forward–backward Runge–Kutta scheme, while the fractional forward Euler method is applied for numerical simulations in MATLAB (R2023a), and bifurcation analysis is conducted using Matcont. Results show that combined control measures markedly increase healthy \(\hbox {CD4}^+\) T-cell counts and reduce viral load, and that fractional order significantly influences system stability, with lower \(\alpha \) promoting faster convergence and higher \(\alpha \) inducing oscillations. Bifurcation analysis reveals transcritical and Hopf bifurcations for specific parameter regimes. Compared with existing studies, the proposed framework integrates immune response, ART-based control, and fractional-order dynamics in a unified setting, providing deeper insight into HIV progression and treatment optimization. Future extensions, including vaccination effects and alternative fractional operators, are also discussed.
