There is still a dramatic increase for using mathematical modelling in the study of epidemiology diseases. Mathematical models were developed to predict how infectious diseases advance to explain the potential outcome of an outbreak, and better facilitate initiatives in global policy. In this article, we present new insights of existence and uniqueness solutions of the novel coronavirus 2019-nCoV/SARS-CoV-2 model via fractional derivatives by using $(\varpi-F_{\mathcal{C}})$-contractions.