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A robust adaptive control is presented for a class of time-varying nonlinear uncertain systems which have a fractional nonlinearly parameterised structure. The proposed design is based on robust adaptive backstepping and neural network approximation. The unknown time-varying parameters in the fractional nonlinear functions are estimated using a smooth projection algorithm and estimation errors are robustly compensated for by the additive terms in the proposed virtual and actual controls. Neural networks are employed to approximate the completely unknown bounding functions of the disturbance terms, and their weights as well as approximation errors are adaptively tuned. It is proved that the proposed robust adaptive control can ensure the semi-global uniform ultimate boundedness of all the closed-loop system signals. The control performance can be improved by an appropriate choice of the design parameters. Simulation results are provided to verify the effectiveness of the proposed design.