The purpose of this paper is to investigate the existence of mild solutions and approximate controllability of a class of multi-term time-fractional measure differential equations of hyperbolic type involving nonlocal conditions in Hilbert spaces. The approximate controllability is demonstrated by utilizing fundamental tools, namely: \((\beta ,\gamma _{k})\)-resolvent family, measure functional (Henstock-Lebesgue-Stieltjes integral), regulated functions and fixed point techniques. Finally, an example is presented.

中文翻译：

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非局部条件下多项时间分数测度微分方程的近似可控性

本文的目的是研究希尔伯特空间中一类涉及非局部条件的双曲型多项时间分数测度微分方程的温和解的存在性和近似可控性。近似可控性通过利用基本工具来证明，即：\((\beta ,\gamma _{k})\) -resolvent family、测量泛函（Henstock-Lebesgue-Stieltjes 积分）、调节函数和不动点技术。最后，给出一个例子。