The AH1N1/09 influenza virus is one of the most dangerous viruses that has greatly affected human life. As it is an unstable virus and new types of it with different features are created every year, its investigation is important. Various mathematical models have been proposed to describe such diseases. In this paper, mathematical modeling in the form of fractional differential equations with the Atangana-Baleanu-Caputo (ABC) derivative and initial value is proposed to study this virus. Since the nature of the virus and how it affects the human body are ambiguous and imprecise, its fuzzy model is discussed. By using tools such as r-cut, generalized Hakuhara difference, ABC fractional derivative in fuzzy mode, and ABC-PI numerical method, the proposed model is solved numerically. At the end, a numerical example is provided to show the applicability of the method. پرونده مقاله