Nowadays, the complete world is suffering from untreated infectious epidemic disease COVID-19 due to coronavirus, which is a very dangerous and deadly viral infection. So, the major desire of this task is to propose some new mathematical models for the coronavirus pandemic (COVID-19) outbreak through fractional derivatives. The adoption of modified mathematical techniques and some basic explanation in this research field will have a strong effect on progressive society fitness by controlling some diseases. The main objective of this work is to investigate the dynamics and numerical approximations for the recommended arbitrary-order coronavirus disease system. This system illustrating the probability of spread within a given general population. In this work, we considered a system of a novel COVID-19 with the three various arbitrary-order derivative operators: Caputo derivative having the power law, Caputo–Fabrizio derivative having exponential decay law and Atangana–Baleanu-derivative with generalized Mittag–Leffler function. The existence and uniqueness of the arbitrary-order system is investigated through fixed-point theory. We investigate the numerical solutions of the non-linear arbitrary-order COVID-19 system with three various numerical techniques. For study, the impact of arbitrary-order on the behavior of dynamics the numerical simulation is presented for distinct values of the arbitrary power β.

中文翻译：

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通过奇异和非奇异分数算子对 COVID-19 模型进行数值研究

如今，全世界都在遭受未经治疗的冠状病毒感染流行病COVID-19，这是一种非常危险且致命的病毒感染。因此，这项任务的主要愿望是通过分数导数提出一些新的冠状病毒大流行（COVID-19）爆发的数学模型。在该研究领域采用改进的数学技术和一些基本解释将通过控制某些疾病对进步社会健康产生重大影响。这项工作的主要目的是研究推荐的任意阶冠状病毒疾病系统的动力学和数值近似。该系统说明了在给定一般人群中传播的概率。在这项工作中，我们考虑了一种新型 COVID-19 系统，具有三种不同的任意阶导数算子：具有幂律的 Caputo 导数、具有指数衰减律的 Caputo-Fabrizio 导数和具有广义 Mittag-Leffler 的 Atangana-Baleanu 导数功能。通过不动点理论研究了任意阶系统的存在唯一性。我们使用三种不同的数值技术研究了非线性任意阶 COVID-19 系统的数值解。为了研究任意阶对动力学行为的影响，针对任意幂β的不同值进行了数值模拟。