The purpose of the current work is to provide the numerical solutions of the fractional mathematical system of the susceptible, infected and quarantine (SIQ) system based on the lockdown effects of the coronavirus disease. These investigations provide more accurateness by using the fractional SIQ system. The investigations based on the nonlinear, integer and mathematical form of the SIQ model together with the effects of lockdown are also presented in this work. The impact of the lockdown is classified into the susceptible/infection/quarantine categories, which is based on the system of differential models. The fractional study is provided to find the accurate as well as realistic solutions of the SIQ model using the artificial intelligence (AI) performances along with the scale conjugate gradient (SCG) design, i.e., AISCG. The fractional-order derivatives have been used to solve three different cases of the nonlinear SIQ differential model. The statics to perform the numerical results of the fractional SIQ dynamical system are 7% for validation, 82% for training and 11% for testing. To observe the exactness of the AI-SCG procedure, the comparison of the numerical attained performances of the results is presented with the reference Adam solutions. For the validation, authentication, aptitude, consistency and validity of the AI-SCG solver, the computing numerical results have been provided based on the error histograms, state transition measures, correlation/regression values and mean square error.