Topological Methods in Nonlinear Analysis

Impulsive problems for fractional evolution equations and optimal controls in infinite dimensional spaces

JinRong Wang, Yong Zhou, and Wei Wei

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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.

Article information

Source
Topol. Methods Nonlinear Anal., Volume 38, Number 1 (2011), 17-43.

Dates
First available in Project Euclid: 20 April 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1461184805

Mathematical Reviews number (MathSciNet)
MR2893622

Zentralblatt MATH identifier
1237.26008

Citation

Wang, JinRong; Zhou, Yong; Wei, Wei. Impulsive problems for fractional evolution equations and optimal controls in infinite dimensional spaces. Topol. Methods Nonlinear Anal. 38 (2011), no. 1, 17--43. https://projecteuclid.org/euclid.tmna/1461184805


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