Stability analysis and optimal control of a fractional-order generalized SEIR model for the COVID-19 pandemic

•A Caputo fractional-order COVID-19 model with generalized incidence rate is established, and some dynamic behaviors are analyzed.•Identify the parameters of the model according to relevant statistical data, which verifies the effectiveness of the model for depicting the COVID-19 pandemic.•Based on the relevant statistical data, the corresponding fractional optimal control problem is proposed and analyzed.•The numerical format of Riemann–Liouville adjoint system with transversality condition is given, and the fractional optimal control problem of the COVID-19 model is solved numerically.