Impulsive problems for fractional evolution equations and optimal controls in infinite dimensional spaces
Keywords
Impulsive fractional evolution equations, $PC$-mild solutions, compactness, existence, continuous dependence, optimal controlsAbstract
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.Downloads
Published
2011-04-23
How to Cite
1.
WANG, JinRong, ZHOU, Yong and WEI, Wei. Impulsive problems for fractional evolution equations and optimal controls in infinite dimensional spaces. Topological Methods in Nonlinear Analysis. Online. 23 April 2011. Vol. 38, no. 1, pp. 17 - 43. [Accessed 19 April 2024].
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