Analysis of a new model of H1N1 spread: Model obtained via Mittag-Leffler function

Abstract

In the recent decades, many physical problems were modelled using the concept of power law within the scope of fractional differentiations. When checking the literature, one will see that there exist many formulas of power law, which were built for specific problems. However, the main kernel used in the concept of fractional differentiation is based on the power law function x-λ. It is quick important to note all physical problems, for instance, in epidemiology. Therefore, a more general concept of differentiation that takes into account the more generalized power law is proposed. In this article, the concept of derivative based on the Mittag-Leffler function is used to model the H1N1. Some analyses are done including the stability using the fixed-point theorem.