Abstract This paper deals with the approximate controllability for a class of fractional stochastic evolution equations with nonlocal initial conditions in a Hilbert space. We delete the compactness condition or Lipschitz condition for nonlocal term appearing in various literatures, and only need to suppose some weak growth condition on the nonlocal term. The discussion is based on the fixed point theorem, diagonal argument and approximation techniques. In the end, an example is presented to illustrate the abstract theory.

中文翻译：

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具有非局部条件的分数阶随机演化方程的近似可控性

摘要 本文研究一类具有非局部初始条件的分数阶随机演化方程在希尔伯特空间中的近似可控性。我们删除了各种文献中出现的非局部项的紧致条件或Lipschitz条件，只需要对非局部项假设一些弱增长条件。讨论基于不动点定理、对角线论证和近似技术。最后，通过一个例子来说明抽象理论。