# Controllability of abstract fractional differential evolution equations with nonlocal conditions

Volume 17, Issue 2, pp 293-300 Publication Date: June 15, 2017
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### Authors

Haiyong Qin - School of Control Science and Engineering, Shandong University, Jinan, Shandong 250061, P. R. China.
Chenghui Zhang - School of Control Science and Engineering, Shandong University, Jinan, Shandong 250061, P. R. China.
Tongxing Li - School of Control Science and Engineering, Shandong University, Jinan, Shandong 250061, P. R. China.
Ying Chen - School of Mathematics, Qilu Normal University, Jinan, Shandong 250013, P. R. China.

### Abstract

In this paper, the controllability of a class of fractional differential evolution equations with nonlocal conditions is investigated. Sufficient conditions which guarantee the controllability of fractional differential evolution equations are obtained. The method used is the contraction mapping principle and Krasnoselskii theorem. A fractional distributed parameter control system is provided to illustrate the applications of our results.

### Keywords

• Fractional differential equation
• controllability
• nonlocal condition
• fixed point theorem.

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