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In this manuscript, a qualitative analysis of the mathematical model of novel coronavirus (COVID-19) involving anew devised fractal-fractional operator in the Caputo sense having the fractional-order q and the fractal dimension p is considered. The concerned model is composed of eight compartments: susceptible, exposed, infected, super-spreaders, asymptomatic, hospitalized, recovery and fatality. When, choosing the fractal order one we obtain fractional order, and when choosing the fractional order one a fractal system is obtained. Considering both the operators together we present a model with fractal-fractional. Under the new derivative the existence and uniqueness of the solution for considered model are proved using Schaefer’s and Banach type fixed point approaches. Additionally, with the help of nonlinear functional analysis, the condition for Ulam’s type of stability of the solution to the considered model …