This article enquires into the state estimation of fractional-order memristive system with discrete time terms. In consideration of the discrete fractional calculus, we present a new efficient condition for the global Mittag-Leffler stability of the estimation error system. Moreover, using a functional that consist by the discrete fractional sum element, the stability condition is also obtained. It is a remarkable fact that the proposed method captures the contribution of a vector optimization method, which gives us a better grip on how to make the convex closure is meaningful. Simulation result is given in the end.