Deterministic and stochastic approaches Hepatitis C model including different fractional operators

This thesis discusses the versions obtained by replacing the classical derivative with fractional derivatives such as Caputo, Caputo-Fabrizio and Atangana-Baleanu in the deterministic and stochastic Hepatitis C model. For the deterministic model, a numerical method based on the Newton polynomial, the positivity of the solutions of the model, the basic reproduction number and is presented, while for the stochastic model, the conditions under which the solution exists and is unique, as well as the associated numerical method for this model, are derived. In addition, the Hepatitis C model is reconstructed using the newly introduced piecewise derivative, which allows the deterministic and stochastic models to be considered together. Some different scenarios are considered for the mentioned models and the numerical simulations of these scenarios obtained using the Matlab program are presented with graphical representations.