Memory properties of fractional-order operators are considered for an input-output data model for highly uncertain nonlinear systems. The model arises by relating the fractional-order variation of the output to the fractional-order variation of the input; the instantaneous gain is computed through a fuzzy inference network, whose output consequences are adapted online on a gradient descent rule. The fractional-order nature of the proposed model relaxes the stringent conditions on data-driven schemes, allowing instantaneous changes in the output signal with a null variation in the controller. The main contribution consists of taking advantage of the memory properties of fractional-order operators and the flexibility of fuzzy logic rules to construct a data-driven model for highly uncertain discrete-time nonlinear systems. The relevance of the proposed method is assessed through experiments in a real-world scenario.