Mean-square pinning control of fractional stochastic discrete-time complex networks

•A new fractional stochastic discrete-time complex networks model is established.•Some pinning controllers and sufficient conditions are given for achieving the mean-square pinning synchronization of the fractional stochastic networks.•Corresponding techniques are extended to solve the synchronization problem of general fractional discrete-time complex networks without noise.•Numerical examples are given to verify the correctness of the obtained theoretical results.