A novel four-dimensional fractional-order chaotic system, which possesses an infinite set of equilibrium points, has been constructed by introducing memristors, with the approximate solution of the system to be obtained based on the Adomian Decomposition Method (ADM). Through Lyapunov exponent spectrum and bifurcation diagram analyses, it is demonstrated that the system exhibits such dynamical behaviors as stable state, period doubling bifurcation, and chaotic state under single parameter variation. An analysis of the Lyapunov exponent distribution diagram, phase diagram, and time series diagram manifests double-vortex scroll chaotic attractors, as well as period-1, and period-2 attractors, under dual parameters in the system. Both Spectral Entropy (SE) and C0 complexity analyses confirm that parameter b exerts a more significant influence on the complexity of the fractional-order Lorenz memristive system.