## Journal of Integral Equations and Applications

### Approximate controllability of impulsive Riemann- Liouville fractional equations in Banach spaces

#### Abstract

In this paper, we study control systems governed by impulsive Riemann-Liouville fractional differential equations in Banach spaces. Firstly, we introduce $PC_{1-\alpha}$-mild solutions for impulsive Riemann-Liouville fractional differential equations. Then, we make a set of assumptions to guarantee the existence and uniqueness of mild solutions. Finally, approximate controllability of the associated impulsive Riemann-Liouville fractional evolution control systems is also formulated and proved.

#### Article information

Source
J. Integral Equations Applications, Volume 26, Number 4 (2014), 527-551.

Dates
First available in Project Euclid: 9 January 2015

Permanent link to this document
https://projecteuclid.org/euclid.jiea/1420812884

Digital Object Identifier
doi:10.1216/JIE-2014-26-4-527

Mathematical Reviews number (MathSciNet)
MR3299830

Zentralblatt MATH identifier
1303.93041

#### Citation

Liu, Zhenhai; Bin, Maojun. Approximate controllability of impulsive Riemann- Liouville fractional equations in Banach spaces. J. Integral Equations Applications 26 (2014), no. 4, 527--551. doi:10.1216/JIE-2014-26-4-527. https://projecteuclid.org/euclid.jiea/1420812884

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