This paper deals with the finite-approximate controllability for a class of fractional stochastic evolution equations with nonlocal initial conditions in a Hilbert space. We establish sufficient conditions for the finite-approximate controllability of the control system when the compactness conditions or Lipschitz conditions for the nonlocal term and uniform boundedness conditions for the nonlinear term are not required. The discussion is based on the fixed point theorem, approximation techniques and diagonal argument. In the end, an example is presented to illustrate the abstract theory. Our result improves and extends some relevant results in this area.

中文翻译：

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具有局部条件的分数阶随机演化方程的有限近似可控性

本文研究了希尔伯特空间中一类具有非局部初始条件的分数阶随机演化方程的有限逼近可控性。当不需要非局部项的紧致性条件或Lipschitz条件和非线性项的均匀有界性条件时，我们为控制系统的有限近似可控性建立了充分的条件。讨论基于不动点定理，逼近技术和对角线论点。最后，给出一个例子来说明抽象理论。我们的结果改进并扩展了该领域的一些相关结果。