Abstract In this paper, we concern with the existence of mild solution to nonlocal initial value problem for nonlinear Sobolev-type impulsive evolution equations with Hilfer fractional derivative which generalized the Riemann–Liouville fractional derivative. At first, we establish an equivalent integral equation for our main problem. Second, by means of the properties of Hilfer fractional calculus, combining measure of noncompactness with the fixed-point methods, we obtain the existence results of mild solutions with two new characteristic solution operators. The results we obtained are new and more general to known results. At last, an example is provided to illustrate the results.

中文翻译：

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非局部条件下脉冲Hilfer分数演化方程的研究

摘要 在本文中，我们关注非线性Sobolev型脉冲演化方程的非局部初值问题的温和解的存在性，该方程具有Hilfer分数阶导数，其推广了Riemann-Liouville分数阶导数。首先，我们为我们的主要问题建立一个等效的积分方程。其次，利用Hilfer分数阶微积分的性质，将非紧性测度与不动点方法相结合，得到具有两个新特征解算子的温和解的存在性结果。我们获得的结果是新的，对已知结果更普遍。最后，提供了一个例子来说明结果。