In the current article, we studied the novel corona virus (2019-nCoV or COVID-19) which is a threat to the whole world nowadays. We consider a fractional order epidemic model which describes the dynamics of COVID-19 under nonsingular kernel type of fractional derivative. An attempt is made to discuss the existence of the model using the fixed point theorem of Banach and Krasnoselskii’s type. We will also discuss the Ulam-Hyers type of stability of the mentioned problem. For semi analytical solution of the problem the Laplace Adomian decomposition method (LADM) is suggested to obtain the required solution. The results are simulated via Matlab by graphs. Also we have compare the simulated results with some reported real data for Commutative class at classical order.

在当前的文章中，我们研究了新型冠状病毒（2019-nCoV或COVID-19），它对当今世界构成威胁。我们考虑一个分数阶流行病模型，该模型描述了分数导数的非奇异核类型下COVID-19的动力学。尝试使用Banach和Krasnoselskii类型的不动点定理讨论模型的存在。我们还将讨论上述问题的Ulam-Hyers型稳定性。对于该问题的半解析解，建议使用拉普拉斯阿德曼分解法（LADM）获得所需的解。结果通过Matlab通过图形进行模拟。我们也将模拟结果与一些经典顺序的交换类报告的实际数据进行了比较。