This present study analyzes COVID-19 transmission using a nonlinear mathematical model with a Caputo fractional derivative. By using fixed point theory, the existence and uniqueness of the solution are examined. We compute the basic reproduction number and investigate the stability analysis of the model. Approximate solutions are obtained using fractional Adam–Bashforth–Moulton method. A comprehensive exploration of optimal control is performed, utilizing one control parameter to investigate the fluctuations in the infected people under some conditions. The simulation results demonstrate the potential of fractional order derivatives with control parameter for a pandemic situation.