A case study of 2019-nCOV cases in Argentina with the real data based on daily cases from March 03, 2020 to March 29, 2021 using classical and fractional derivatives.

In this study, our aim is to explore the dynamics of COVID-19 or 2019-nCOV in Argentina considering the parameter values based on the real data of this virus from  03, 2020 to  29, 2021 which is a data range of more than one complete year. We propose a Atangana-Baleanu type fractional-order model and simulate it by using predictor-corrector (P-C) method. First we introduce the biological nature of this virus in theoretical way and then formulate a mathematical model to define its dynamics. We use a well-known effective optimization scheme based on the renowned trust-region-reflective (TRR) method to perform the model calibration. We have plotted the real cases of COVID-19 and compared our integer-order model with the simulated data along with the calculation of basic reproductive number. Concerning fractional-order simulations, first we prove the existence and uniqueness of solution and then write the solution along with the stability of the given P-C method. A number of graphs at various fractional-order values are simulated to predict the future dynamics of the virus in Argentina which is the main contribution of this paper.