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

نوع مقاله : مقاله پژوهشی

نویسندگان
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
چکیده
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.
کلیدواژه‌ها
Lipschitz property
Fixed point
$\alpha$-$\psi$ contractions
Mathematical modeling
existence and uniqueness
مجله هندسه دیفرانسیل، کاربردها و جنبه‌ها
دوره 1، شماره 1
زمستان 1402
صفحه 49-58

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