The existence and uniqueness of mild solutions for a fractional stochastic differential system derived by Atangana–Baleanu fractional derivative have been discussed in a Hilbert space. A new set of results is obtained with non-Lipschitz conditions of nonlinear functions using the well-known Picard-type iterations, basic concepts of fractional calculus, sectorial operator, and stochastic analysis techniques. At last, an application is discussed to show the applicability of the developed theory.

中文翻译：

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具有非Lipschitz条件的随机微分系统的一些存在性结果

在希尔伯特空间中讨论了由 Atangana-Baleanu 分数导数导出的分数随机微分系统的温和解的存在性和唯一性。使用众所周知的 Picard 型迭代、分数阶微积分的基本概念、扇形算子和随机分析技术，在非线性函数的非 Lipschitz 条件下获得了一组新的结果。最后，讨论了一个应用程序，证明了所发展理论的适用性。