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This paper introduces a novel neural network adaptive fractional-order sliding mode control strategy based on the minimal learning parameter method (MLPNN-FOSMC). This method aims to solve the problem of relative position control in satellite formation flying (SFF), especially in the presence of model uncertainties, external disturbances, input saturation, and unknown actuator gains. First, the mathematical model for satellite relative positioning is derived. Then, a fractional-order sliding mode controller is introduced and integrated with a radial basis function (RBF) neural network and the minimal learning parameter (MLP) strategy to compensate for errors caused by model uncertainties and external disturbances. At the same time, adaptive control is employed to mitigate the impact of unknown actuator gains on the system. To address the non-smooth input saturation nonlinearity problem, a new saturation function with the smoothing properties of the hyperbolic tangent function is introduced. The system’s stability is ensured by employing the Lyapunov theorem. Finally, a comparative analysis with traditional sliding mode control (SMC) and neural network sliding mode control based on minimal learning parameter (MLPNN-SMC) highlights the superiority of the proposed method.