Impulsive problems for fractional evolution equations and optimal controls in infinite dimensional spaces - Wang, JinRong; Zhou, Yong; Wei, Wei (Topological Methods in Nonlinear Analysis, 2011)
In this paper, a class of impulsive fractional evolution equations and optimal controls in infinite dimensional spaces is considered. A suitable concept of a PC-mild solution is introduced and a suitable operator mapping is also constructed. By using a PC-type Ascoli-Arzela theorem, the compactness of the operator mapping is proven. Applying a generalized Gronwall inequality and Leray-Schauder fixed point theorem, the existence and uniqueness of the PC-mild solutions is obtained. Existence of optimal pairs for system governed by impulsive fractional evolution equations is also presented. Finally, an example illustrates the applicability of our results.