We introduce the investigation of approximate controllability for a new class of nonlocal and noninstantaneous impulsive Hilfer fractional neutral stochastic integrodifferential equations with fractional Brownian motion. An appropriate set of sufficient conditions is derived for the considered system to be approximately controllable. For the main results, we use fractional calculus, stochastic analysis, fractional power of operators and Sadovskii’s fixed point theorem. At the end, an example is also given to show the applicability of our obtained theory.

中文翻译：

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具有分数布朗运动的非瞬时脉冲Hilfer分数阶积分微分方程的近似可控性

我们介绍了一类新的具有分数布朗运动的新型非局部和非瞬时脉冲Hilfer分数中性随机积分微分方程的近似可控性。得出适当的一组充分条件，以使所考虑的系统近似可控。对于主要结果，我们使用分数演算，随机分析，算子的分数幂和Sadovskii不动点定理。最后，通过一个例子说明了所获得理论的适用性。