This work is devoted to study the uncertain attacking behavior of computer viruses in wireless sensor network involving fuzzy fractional derivatives with non-local Mittag-Leffler function kernel. Based on epidemic theory and fractional calculus, we propose a fuzzy fractional Susceptible – Infectious – Quarantine – Recovered (SIQR) model to describe dynamics of virus propagation with quarantine in the network. The concept of Atangana–Baleanu fuzzy fractional derivative in Caputo sense is proposed with some important properties to investigate the fractional SIQR model with fuzzy data. The fuzzy Laplace transform of Atangana–Baleanu derivative is proposed to represent the analytic mild solutions of the fractional SIQR model. Then, the existence and uniqueness of mild solutions is proved by using generalized contraction principle. An efficient numerical scheme to solve numerical solutions of the fractional SIQR model is introduced. Finally, some graphical representations are given to show the uncertain attack behavior of computer virus and dynamical behavior of the model.

这项工作致力于研究带有模糊分数导数和非局部Mittag-Leffler函数核的无线传感器网络中计算机病毒的不确定攻击行为。基于流行病学理论和分数演算，我们提出了一种模糊分数敏感-传染性-检疫-恢复（SIQR）模型来描述网络中检疫的病毒传播动态。提出了Caputo意义上的Atangana–Baleanu模糊分数导数的概念，该概念具有重要的性质，可用于研究带有模糊数据的分数SIQR模型。提出了Atangana–Baleanu导数的模糊Laplace变换来表示分数SIQR模型的解析温和解。然后，利用广义压缩原理证明了温和解的存在性和唯一性。介绍了一种解决分数SIQR模型数值解的有效数值方案。最后，给出了一些图形表示，以显示计算机病毒的不确定攻击行为和模型的动态行为。