In this paper, we study the controllability and optimal control for a class of time-delayed fractional stochastic integro-differential system with Poisson jumps. A set of sufficient conditions is established for complete and approximate controllability by assuming non-Lipschitz conditions and pth mean square norm. We also give an existence of optimal control for Bolza problem. Our result is valid for fractional order \(\alpha >\frac{p-1}{p},\ p\ge 2.\) Finally, an example is provided to illustrate the efficiency of the obtained theoretical results.

中文翻译：

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一类时滞分数阶整数积分微分系统的可控性和最优控制

本文研究了一类带有泊松跳跃的时滞分数阶随机积分-微分系统的可控性和最优控制。通过假设非Lipschitz条件和pth均方范数，可以为完全和近似可控性建立一套充分的条件。我们还给出了Bolza问题的最优控制的存在。我们的结果对于分数阶\（\ alpha> \ frac {p-1} {p}，\ p \ ge 2. \）是有效的。最后，提供了一个例子来说明所获得理论结果的效率。