Mathematical analysis of a coronavirus model with Caputo, Caputo–Fabrizio–Caputo fractional and Atangana–Baleanu–Caputo differential operators

Abstract

This research aims to use fractional operators to analyze a fractional-order model of a coronavirus disease of 2019 (COVID-19). We use some basic results and definitions from fractional calculus and then, by using them, investigate the effects of these operators in a better elucidation of the epidemic COVID-19. We showed the existence and uniqueness of the solution of the proposed model by applying the Picard–Lindelöf theorem and Banach contraction principle. We established the generalized Hyers–Ulam stability of the fractional model using Gronwall’s inequality. We developed effective numerical scheme to solve these fractional systems, which gives a perfect approximate solution to the fractional system. Finally, the numerical simulations were performed in each case to verify all theoretical result.