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In this paper,coexistence and local Mittag-Leffler stability of fractional-order recurrent neural networks with discontinuous activation functions are addressed.Because of the discontinuity of the activation function,Filippov solution of the neural network is defined.Based on Brouwer’s fixed point theorem and definition of Mittag-Leffler stability,sufficient criteria are established to ensure the existence of (2k + 3)n (k ≥ 1) equilibrium points,among which (k + 2)n equilibrium points are locally Mittag-Leffler stable.Compared with the existing results,the derived results cover local Mittag-Leffler stability of both fractional-order and integral-order recurrent neural networks.Meanwhile discontinuous networks might have higher storage capacity than the continuous ones.Two numerical examples are elaborated to substantiate the effective of the theoretical results.