Averaging of neutral stochastic partial functional differential equations involving delayed impulses

In this paper, we initiate a study on averaging principles for neutral stochastic partial functional differential equations (NSPFDEs) with delayed impulses. With the aid of inequality techniques, the semigroup approach and some technical transformations, we derive an averaging principle for a class of NSPFDEs involving delayed impulses. The results obtained ensure that one can focus on the averaged autonomous system without impulses in place of the original system, thus providing an effective way for reducing complexity. In the end, an example is worked out to demonstrate the theoretical results.