Impulsive problems for fractional evolution equations and optimal controls in infinite dimensional spaces
Słowa kluczowe
Impulsive fractional evolution equations, $PC$-mild solutions, compactness, existence, continuous dependence, optimal controlsAbstrakt
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.Pobrania
Opublikowane
2011-04-23
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1.
WANG, JinRong, ZHOU, Yong & WEI, Wei. Impulsive problems for fractional evolution equations and optimal controls in infinite dimensional spaces. Topological Methods in Nonlinear Analysis [online]. 23 kwiecień 2011, T. 38, nr 1, s. 17–43. [udostępniono 22.7.2024].
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