This article studies sensitivity properties of optimal control problems that are governed by nonlinear Hilfer fractional evolution inclusions (NHFEIs) in Hilbert spaces, where the initial state \(\xi \) is not the classical Cauchy, but is the Riemann–Liouville integral. First, we obtain the nonemptiness and the compactness properties of mild solution sets \(\mathbb {S}(\xi )\) for NHFEIs, and also establish an extension Filippov’s theorem. Then we obtain the continuity and upper semicontinuity of optimal control problems connected with NHFEIs depending on a initial state \(\xi \) as well as a parameter \(\lambda \). Finally, An illustrating example is given.

本文研究了由希尔伯特空间中的非线性希尔弗分数演化包含物（NHFEIs）控制的最优控制问题的敏感性，其中初始状态\（\ xi \）不是经典柯西，而是黎曼–利维尔积分。首先，我们获得了NHFEI的温和解集\（\ mathbb {S}（\ xi）\）的非空性和紧性，并建立了Filippov定理的扩展。然后，我们根据初始状态\（\ xi \）以及参数\（\ lambda \）获得与NHFEI相关的最优控制问题的连续性和上半连续性。最后，给出一个说明性的例子。