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In this paper, new model on novel coronavirus disease (COVID-19) with four compartments including susceptible, exposed, infected, and recovered class with fractal-fractional derivative is proposed. Here, Banach and Leray–Schauder alternative type theorems are used to establish some appropriate conditions for the existence and uniqueness of the solution. Also, stability is needed in respect of the numerical solution. Therefore, Ulam–Hyers stability using nonlinear functional analysis is used for the proposed model. Moreover, the numerical simulation using the technique of fundamental theorem of fractional calculus and the two-step Lagrange polynomial known as fractional Adams-Bashforth (AB) method is proposed. The obtained results are tested on real data of COVID-19 outbreak in Malaysia from 25 January till 10 May 2020. The numerical simulation of the proposed model has performed in terms of graphs for …