This article is primarily focusing on the existence of Sobolev‐type Hilfer fractional neutral integro‐differential systems via measure of noncompactness. We study our primary outcomes by employing fractional calculus, measure of noncompactness and fixed point technique. First, we discuss the existence of mild solution for the fractional evolution system. Then, we extend our results to discuss the system with nonlocal conditions. Finally, we provide theoretical and practical applications to illustrate the obtained theory.

中文翻译：

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无限时延Sobolev型Hilfer分数中立积分微分方程存在性的新探索

本文主要通过非紧缩性度量来研究Sobolev型Hilfer分数中性积分微分系统的存在。我们通过采用分数演算，非紧致性度量和定点技术来研究我们的主要结果。首先，我们讨论分数演化系统的温和解的存在。然后，我们扩展结果以讨论具有非本地条件的系统。最后，我们提供理论和实际应用来说明所获得的理论。