Aim of this article is to analyze the fractional order computer epidemic model. To this end, a classical computer epidemic model is extended to the fractional order model by using the Atangana–Baleanu fractional differential operator in Caputo sense. The regularity condition for the solution to the considered system is described. Existence of the solution in the Banach space is investigated and some benchmark results are presented. Steady states of the system is described and stability of the model at these states is also studied, with the help of Jacobian matrix method. Some results for the local stability at disease free equilibrium point and endemic equilibrium point are presented. The basic reproduction number is mentioned and its role on stability analysis is also highlighted. The numerical design is formulated by applying the Atangana–Baleanu integral operator. The graphical solutions are also presented by computer simulations at both the equilibrium points.

中文翻译：

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分数阶计算机病毒流行模型的最优存在性及数值模拟

本文的目的是分析分数阶计算机流行病模型。为此，通过使用 Caputo 意义上的 Atangana-Baleanu 分数阶微分算子，将经典的计算机流行病模型扩展到分数阶模型。描述了所考虑系统的解的规律性条件。研究了 Banach 空间中解的存在性，并给出了一些基准结果。在雅可比矩阵方法的帮助下，描述了系统的稳态，并研究了模型在这些状态下的稳定性。给出了无病平衡点和地方病平衡点局部稳定性的一些结果。提到了基本再生数，并强调了它在稳定性分析中的作用。数值设计是通过应用 Atangana-Baleanu 积分算子制定的。图形解也通过在两个平衡点的计算机模拟来呈现。