In this work, a fractional Hénon memristor model is studied, with a systematic analysis of its dynamic response under both commensurate and incommensurate orders. Extensive numerical methods, such as phase portraits, bifurcation plots, Lyapunov exponents, sample entropy, and \(C_0\) complexity, are utilized to investigate the system’s chaotic characteristics and quantify its complexity. Notably, the nonexistence of stationary states in the introduced fractional map gives rise to a variety of hidden dynamic behaviors, contributing to the emergence of intricate, fractal-like chaotic attractors. Our results demonstrate a strong sensitivity of the system’s dynamics to changes in the fractional parameters, leading to diverse and rich behavior. The layered construction and rich dynamics of the memristor chaotic system make it a promising candidate for further studies in nonlinear science and fractional-order modeling.