This chapter delves into the rich and intricate dynamical behaviors of memristor-based discrete model influenced by fractional-order calculus. Recognized for their emerged as pivotal components in modern computing and memory technologies due to their unique properties and transformative potential. Their integration into nonlinear dynamical systems has sparked significant interest, particularly in the study of complex and chaotic behaviors. The study systematically examines three core models: systems governed by commensurate fractional orders, incommensurate fractional orders, and those incorporating variable fractional orders. Each variant exhibits distinct dynamical properties, including the emergence of complex hyperchaotic behavior and hidden attractors, even in the absence of fixed points. Through a robust combination of rigorous numerical analysis, employing bifurcation diagrams, phase portraits, and Lyapunov exponent calculations, the chaotic nature of these systems is systematically validated. Numerical simulations further reinforce the theoretical predictions, ensuring robustness and reproducibility.