Abstract
Our main aim in this article is to introduce and investigate a new model of fractional-order model for hepatitis C virus (HCV) infection with immune response, in which the effect of dendritic cells (DC) and cytotoxic T lymphocytes (CTL) on HCV infection is considered. In the first stage, the HCV model was extended to Liouville-Caputo (LC) fractional derivative and Caputo-Fabrizio fractional derivative in the Caputo sense (CFC). In particular, we evaluate the approximate solutions of this model by means of the power law and the exponential law kernel. The approximate solutions are based upon the fundamental theorem of fractional calculus as well as the Lagrange polynomial interpolation. We study the effect of the variation the fractional-order on the behavior of the solutions due to the presence of definitions of new fractional-calculus operators. We observe that the chaotic behavior and illustrate the chaotic of a chronic HCV infection model with immune response by plotting the solutions in the plane. Finally, some numerical simulations using with the aid of Mathematica were done for different values of fractional order. (C) 2020 Elsevier Ltd. All rights reserved.