This paper deals with a numerical simulation of fractional conformable attractors of type Rabinovich–Fabrikant, Thomas’ cyclically symmetric attractor and Newton–Leipnik. Fractional conformable and $\beta$ -conformable derivatives of Liouville–Caputo type are considered to solve the proposed systems. A numerical method based on the Adams–Moulton algorithm is employed to approximate the numerical simulations of the fractional-order conformable attractors. The results of the new type of fractional conformable and $\beta$ -conformable attractors are provided to illustrate the effectiveness of the proposed method.