This chapter presents an investigation into the dynamics of a newly developed fractional-order Ikeda-based memristive map, explored under the commensurate fractional-order setting. Constructed through the Caputo-type delta differencesf, the model integrates memory effects and fractional dynamics into a discrete-time chaotic framework. The analysis focuses exclusively on the commensurate case, where all fractional orders are equal, offering insights into the influence of fractional order on system behavior. A combination of numerical techniques such as bifurcation diagrams, Lyapunov exponent analysis, and phase portraits, is employed to reveal transitions between periodicity and chaos. To evaluate the system’s intrinsic complexity, we apply the sample entropy method, the 0–1 test for chaos, and the \(C_0\) complexity indicator. The findings emphasize the enhanced complexity brought by fractional dynamics, particularly in the presence of memristive elements, thereby opening new avenues for research in discrete-time fractional-order chaotic systems.