In this paper, we investigate the existence and stability of solutions for a class of optimal control problems with 1-mean equicontinuous controls, and the corresponding state equation is described by non-instantaneous impulsive differential equations. The existence theorem is obtained by the method of minimizing sequence, and the stability results are established by using the related conclusions of set-valued mappings in a suitable metric space. An example with the measurable admissible control set, in which the controls are not continuous, is given in the end.

This paper is intended as an attempt to investigate the existence and stability of solutions for a class of fractional optimal control problems characterized with non-instantaneous impulsive differential equations. By using the method of minimizing sequence and the related conclusions of set-valued mapping, the results of solvability and stability for a class of optimal control problems are obtained in the suitable metric space.