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Although stochastic gradient algorithm can identify linear systems with high efficiency. It is inefficient for nonlinear systems for the difficulty in the step-size designing. To overcome this dilemma, this paper proposes a fractional stochastic gradient algorithm for systems with piece-wise linear input. First, the nonlinear system is transformed into a polynomial nonlinear model, then the parameters and time-delay are estimated iteratively based on the fractional stochastic gradient algorithm and self-organizing maps method. In addition, to increase the convergence rates of the fractional stochastic gradient algorithm, a multi-innovation fractional stochastic gradient algorithm is developed. Convergence analysis and simulation examples are introduced to show the effectiveness of the proposed algorithms.