Numerical Treatment for Solving Fractional Optimal Control Problems Related to AH1N1/09 Influenza

In this research, we develop a fractional‐order mathematical model for the AH1N1/09 virus by introducing a control variable u ( t ) representing vaccination. The model is transformed from its integer‐order form to a fractional‐order framework using the Caputo derivative. The control variable is designed to maximize the recovery rate of individuals infected with AH1N1/09 influenza. For the proposed model, we examine the existence and uniqueness of the solution and establish their positivity and boundedness. We then derive the optimality system (OS) and solve the fractional optimal control problem using Pontryagin’s maximum principle (PMP). Numerical solutions are obtained via the generalized Euler’s method (GEM) and the iterative optimal control method (IOCM). Comparative results across different fractional orders demonstrate that GEM outperforms IOCM in terms of efficiency.