On the study of stochastic fractional-order differential equation systems

Abstract

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.