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 $\varphi -\psi$-contractions and $\varphi$-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.

在本文中，我们在由易感人群、暴露人群、传染人群和康复人群组成的四类框架内，制定了一种名为 AH1N1/09​​ 的特定类型流感病毒的新模型。第一次，我们在高级算子的帮助下研究了这个模型，该算子通过幂律类型内核具有两个分形和分数阶的分形-分数算子。AH1N1/09​​ 的分形-分形模型的解的存在性通过一些特殊的映射来研究，例如$\phi -\psi$- 宫缩和$\phi$- 准入。Leray-Schauder 定理也适用于此目的。在研究了四个版本的稳定性标准后，为了逼近所需的数值解，我们实施了 Adams-Bashforth (AB) 方案，并模拟了分形和分数阶的不同数据的图形。最后，我们通过广义 Liouville-Caputo 型（GLC 型）算子将分形-分形 AH1N1/09​​ 模型转换为分数模型，然后模拟由称为 Kumar-Erturk 方法的新数值方案引起的新图。