## Abstract and Applied Analysis

### The Solvability and Optimal Controls for Some Fractional Impulsive Equation

#### Abstract

This paper is concerned with the existence and uniqueness of mild solution of some fractional impulsive equations. Firstly, we introduce the fractional calculus, Gronwall inequality, and Leray-Schauder’s fixed point theorem. Secondly with the help of them, the sufficient condition for the existence and uniqueness of solutions is presented. Finally we give an example to illustrate our main results.

#### Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 914592, 9 pages.

Dates
First available in Project Euclid: 27 February 2014

https://projecteuclid.org/euclid.aaa/1393512087

Digital Object Identifier
doi:10.1155/2013/914592

Mathematical Reviews number (MathSciNet)
MR3121409

Zentralblatt MATH identifier
07095486

#### Citation

Liu, Xianghu; Liu, Zhenhai; Han, Jiangfeng. The Solvability and Optimal Controls for Some Fractional Impulsive Equation. Abstr. Appl. Anal. 2013 (2013), Article ID 914592, 9 pages. doi:10.1155/2013/914592. https://projecteuclid.org/euclid.aaa/1393512087

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