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

Afshari, Hojjat; Ahadi, Leila

doi:10.22034/jdgaa.2024.2037283.1010

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

Document Type : Original Article

Authors

Hojjat Afshari ¹

Leila Ahadi ²

¹ Department of Mathematics and Computer Sciences, Basic Sciences Faculty, University of Bonab, Bonab, Iran.

² {Miandoab County Education Department, West Azarbaijan, Miandoab, Iran.

10.22034/jdgaa.2024.2037283.1010

Abstract

This paper proposes a novel model for the dynamics of susceptible, exposed, infectious, and recovered individuals infected with the AH1N1/09 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