This article is devoted to studying the topological structure of a solution set for Clarke subdifferential type fractional non-instantaneous impulsive differential inclusion driven by Poisson jumps. Initially, for proving the solvability result, we use a nonlinear alternative of Leray–Schauder fixed point theorem, Gronwall inequality, stochastic analysis, a measure of noncompactness, and the multivalued analysis. Furthermore, the mild solution set for the proposed problem is demonstrated with nonemptyness, compactness, and, moreover, \(R_\delta \)-set. By employing Balder’s theorem, the existence of optimal control is derived. At last, an application is provided to validate the developed theoretical results.

本文致力于研究泊松跳跃驱动的Clarke次微分型分数阶非瞬时脉冲微分包含解的解集的拓扑结构。最初，为了证明可解性结果，我们使用Leray–Schauder不动点定理，Gronwall不等式，随机分析，非紧致性度量和多值分析的非线性替代方法。此外，针对所提出问题的温和解集通过非空性，紧致性以及\（R_ \ delta \） -集得到证明。通过使用巴尔德定理，得出最优控制的存在。最后，提供了一个应用程序来验证所开发的理论结果。