In this article, we establish some sufficient conditions for total controllability of a neutral fractional differential system with impulsive conditions in the finite-dimensional spaces. This type of controllability concerns the controllability problem not only at the final time but also at the impulse time. We use Mittag-Leffler matrix function, nonlinear functional analysis, controllability Grammian type matrices and fixed point theorem due to Krasnoselskii’s to establish these results. Also, we extend these results for the studied problem with the integro term. At last, some simulated examples are given to validate the obtained results.

中文翻译：

---

具有非瞬时脉冲效应的中立型分数阶微分方程的总可控性

在本文中，我们为有限维空间中具有脉冲条件的中立分数阶微分系统的总可控性建立了一些充分条件。这种类型的可控性不仅在最终时间而且在脉冲时间都涉及可控性问题。我们使用Mittag-Leffler矩阵函数，非线性泛函分析，可控制的Grammian型矩阵和由于Krasnoselskii导致的不动点定理来建立这些结果。同样，我们将这些结果扩展为整数项所研究的问题。最后，给出了一些仿真实例来验证所获得的结果。