In recent decades, researchers have focused on chaotic systems and have increasingly attracted their interest. More specifically, chaotic systems based on memristors, which constitute the \(4^{th}\) essential component added to resistors, capacitors, and inductors, have attracted even more attention from scientists due to their properties. In this paper, we propose a new memristive chaotic system of fractional-order. To investigate the dynamic properties of the proposed system, thorough analysis was conducted on its equilibrium points and their stability. To scrutinize the performance of the showcased model, the Lyapunov characteristic exponents and the bifurcation diagram were given....