Some novel mathematical analysis on the fractal–fractional model of the AH1N1/09 virus and its generalized Caputo-type version

In this paper, we formulate a new model of a particular type of influenza virus called AH1N1/09 in the framework of the four classes consisting of susceptible, exposed, infectious and recovered people. For the first time, we here investigate this model with the help of the advanced operators entitled the fractal–fractional operators with two fractal and fractional orders via the power law type kernels. The existence of solution for the mentioned fractal–fractional model of AH1N1/09 is studied by some special mappings such as ϕ−ψ-contractions and ϕ-admissibles. The Leray–Schauder theorem is also applied for this aim. After investigating the stability criteria in four versions, to approximate the desired numerical solutions, we implement Adams–Bashforth (AB) scheme and simulate the graphs for different data on the fractal and fractional orders. Lastly, we convert our fractal–fractional AH1N1/09 model into a fractional model via the generalized Liouville–Caputo-type (GLC-type) operators and then, we simulate new graphs caused by the new numerical scheme called Kumar–Erturk method.