This paper investigates a new model on coronavirus-19 disease (COVID-19) with three compartments including susceptible, infected, and recovered class under Mittag-Leffler type derivative. The mentioned derivative has been introduced by Atangana, Baleanu, and Caputo abbreviated as \((\mathcal{ABC})\). Upon utilizing fixed point theory, we first prove the existence of at least one solution for the considered model and its uniqueness. Also, some results about stability of Ulam–Hyers type are also established. By applying a numerical technique called fractional Adams–Bashforth (AB) method, we develop a scheme for the approximate solutions to the considered model. Using some real available data, we perform the concerned numerical simulation corresponding to different values of fractional order.

本文研究了一种新的冠状病毒19疾病模型（COVID-19），该模型在Mittag-Leffler类型衍生物的作用下分为易感，感染和恢复类三个部分。提到的派生词由Atangana，Baleanu和Caputo引入，缩写为\（（\ mathcal {ABC}）\）。利用定点理论，我们首先证明了所考虑模型及其唯一性的至少一个解决方案的存在。此外，还建立了有关Ulam-Hyers型稳定性的一些结果。通过应用称为分数Adams–Bashforth（AB）方法的数值技术，我们为所考虑模型的近似解决方案开发了一种方案。使用一些实际可用数据，我们执行了与分数阶不同值相对应的相关数值模拟。