Some existence and uniqueness results of the mathematical modeling for a particular type of influenza virus by the Fractal-Fractional derivative

This paper proposes a novel model for the dynamics of susceptible, exposed, infectious, and recovered individuals infected with the AH۱N۱/۰۹ influenza strain. The model leverages fractal-fractional operators with power-law kernels to capture the inherent memory effects and complex transmission patterns associated with the virus. We establish existence criteria using two approaches to analyze the qualitative behavior of the model's solutions. Firstly, we demonstrate the existence of solutions through the concept of \alpha-\psi contractions and \alpha-admissible mappings. Secondly, we employ the Leray-Schauder theorem to provide an alternative existence condition. Finally, the uniqueness of the solution is investigated by exploiting the Lipschitz property.

Keywords:

Lipschitz property , Fixed point , \alpha-\psi contractions , Mathematical modeling , Existence and uniqueness