Abstract
In this research, we examine the nonsingular memory effect when implementing the Atangana–Baleanu (AB) fractional derivative in the Caputo sense to the Hepatitis C virus (HCV) model. For this purpose, first, the sufficient conditions for the existence and uniqueness of the solutions under the AB fractional derivative of the model are expressed and proved. Therewithal, in order to show the response of the AB derivative on the system dynamics practically, a new version of the predictor–corrector method is used with the newly estimated model parameters from the literature. Finally, we provide some simulations of the results.