Abstract The aim of this study is to investigate the finite approximate controllability of certain Hilfer fractional evolution systems with nonlocal conditions. To achieve this, we first transform the mild solution of the Hilfer fractional evolution system into a fixed point problem for a condensing map. Then, by using the topological degree approach, we present sufficient conditions for the existence and uniqueness of the solution of the Hilfer fractional evolution systems. Using the variational approach, we obtain sufficient conditions for the finite approximate controllability of semilinear controlled systems. Finally, an example is provided to illustrate main results.

中文翻译：

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具有非局部条件的 Hilfer 分数演化系统的有限近似可控性

摘要 本研究的目的是研究具有非局部条件的某些 Hilfer 分数演化系统的有限近似可控性。为了实现这一点，我们首先将 Hilfer 分数演化系统的温和解转化为凝聚图的不动点问题。然后，利用拓扑度方法，我们给出了Hilfer分数进化系统解的存在唯一性的充分条件。使用变分方法，我们获得了半线性受控系统有限近似可控性的充分条件。最后，提供了一个例子来说明主要结果。