Abstract
We explore a new kind of second-order impulsive stochastic differential system with delays. By using the Hausdorff measure of noncompactness and Mnch fixed point theorem, we investigated the existence of mild solution for the considered systems. Further, we proved the existence of optimal control of the proposed system by using minimizing sequence, Lagrange functional, and Marzur lemma. An example is provided to validate the obtained results.
Acknowledgments
We are very thankful to the anonymous reviewers and associate editor for their constructive comments and suggestions which help us to improve the manuscript.
Disclosure statement
No potential conflict of interest was reported by the author(s).