Abstract
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.
Citation
JinRong Wang. Yong Zhou. Wei Wei. "Impulsive problems for fractional evolution equations and optimal controls in infinite dimensional spaces." Topol. Methods Nonlinear Anal. 38 (1) 17 - 43, 2011.
Information