In this chapter, we examine the implementation of a non-linear control rule for stabilizing 2D fractional chaotic memristive map defined by the Caputo-like difference operator. Firstly, we introduced some basic linear control rules to regulate the dynamics of the 2D fractional chaotic memory map. In the context of the discrete fractional calculus, The suggested fractional memristive map’s nonlinear dynamics are examined using a number of numerical methods, such as phase attractors, Lyapunov exponents, and bifurcation diagrams. By altering the fractional orders, we have demonstrated that the model have rich dynamics such as strange chaotic attractors, period-doubling bifurcation, transient states, and multistability. Furthermore, we present various appropriate techniques to stabilize the fractional chaotic memrsitive map by the use of adaptive non-linear controllers. The results were acquired by employing the stabilization conditions theorem and the properties of the Caputo-like difference operator. Finally, the validity of the constructed non-linear controllers is confirmed by applying pertinent simulation data.