  In this article, the existence and uniqueness about the solution for a class
of stochastic fractional-order differential equation systems are investigated,
where the fractional derivative is described in Caputo sense. The fractional
calculus, stochastic analysis techniques and the standard Picard's iteration
are used to obtain the required results, the nonlinear term is satisfied with
some non-Lipschitz conditions (where the classical Lipschitz conditions are
special cases). The stochastic fractional-order Newton-Leipnik and Lorenz
systems are provided to illustrate the obtained theory, and numerical
simulation results are also given by the modified Adams predictor-corrector
scheme.
