The aim of this article is to modeling khat chewing dynamics using the Caputo and Caputo–Fabrizio fractional operators. We apply the new fractional two-step Adams–Bashforth schemes for the approximation of these derivatives. These numerical schemes are formulated by combining the fundamental theorem of fractional calculus with the two-step Lagrange polynomial. The stability analysis of equilibrium points for a fractional derivative of the model was checked. The Existence and uniqueness of solutions of fractional dynamic were as proved by adopting the fixed point theorem. Numerical simulations for various \(\theta\) values are carried out for the analysis of khat chewing dynamics.