This study develops a fractional-order model for Human Papillomavirus (HPV) transmission and cervical cancer progression within the Atangana-Baleanu-Caputo (ABC) framework. The model incorporates five optimal control strategies: public health education, prophylactic vaccination, early screening of asymptomatic infections, therapeutic vaccination, and treatment of invasive cervical cancer. Qualitative analysis establishes the controlled reproduction number \(R_c\), showing that the disease-free equilibrium is locally asymptotically stable when \(R_c<1\), with a forward bifurcation at \(R_c=1\). Sensitivity analysis identifies the effective transmission rate and asymptomatic individuals as key drivers of transmission. The model is solved numerically using the Adams-Bashforth-Moulton predictor-corrector scheme, while optimal controls are obtained via the Forward-Backward Sweep Method. Simulations for fractional orders \((\nu = 0.7, 0.8, 0.9, 1.0)\) reveal the impact of memory effects on disease dynamics. Individual interventions yield moderate reductions in the objective functional, with screening (\(30.8\%\)) outperforming vaccination (\(26.9\%\)) and education (\(15.4\%\)). Sensitivity analysis shows that screening is two to three times more effective than vaccination. Combined interventions produce the greatest impact, achieving up to \(68.1\%\) reduction. Without control, the epidemic peaks at 4.2 years with approximately 285,000 cases, while full intervention reduces the peak by \(70.5\%\), shifts it to 2.8 years, and lowers the final burden to about 85,000 cases. Overall, the results demonstrate that fractional-order optimal control models effectively capture memory effects and highlight the critical role of asymptomatic carriers. The findings support prioritizing screening alongside vaccination, education, therapeutic vaccination, and treatment to significantly reduce HPV transmission and cervical cancer burden.
