Optimal control problem for higher-order non-instantaneous impulsive fractional system with non-local conditions

The purpose of this article is to study the optimal control problem of higher-order non-instantaneous impulsive fractional system with non-local conditions by virtue of cosine operator theory in the Hilbert space. Initially, the sufficient conditions for the existence of a mild solution of the proposed system are verified by applying the fixed point theorem in infinite dimensional space. Further, we formulate and prove the existence results for optimal control of the proposed system with the corresponding cost functional by using Balder's theorem. Finally, an example is provided to illustrate the main results.