In this paper, we present a reliable multistep numerical approach, so-called Multistep Generalized Differential Transform (MsGDT), to obtain accurate approximate form solution for Rabinovich–Fabrikant model involving Caputo fractional derivative subjected to appropriate initial conditions. The solution methodology provides efficiently convergent approximate series solutions with easily computable coefficients without employing linearization or perturbation. The behavior of approximate solution for different values of fractional-order is shown graphically. Furthermore, the stability analysis of the suggested model is discussed quantitatively. Simulation of the MsGDT technique is also presented to show its efficiency and reliability. Numerical results indicate that the method is simple, powerful mathematical tool and fully compatible with the complexity of such problems.