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Journal of Function Spaces
Volume 2017, Article ID 2508165, 7 pages
https://doi.org/10.1155/2017/2508165
Research Article

Approximate Controllability for Functional Equations with Riemann-Liouville Derivative by Iterative and Approximate Method

School of Mathematical Sciences, Yangzhou University, Yangzhou, Jiangsu 225002, China

Correspondence should be addressed to Gang Li; nc.ude.uzy@ilg

Received 31 March 2017; Accepted 28 May 2017; Published 27 June 2017

Academic Editor: Lishan Liu

Copyright © 2017 Badawi Hamza Elbadawi Ibrahim et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We discuss the functional control systems governed by differential equations with Riemann-Liouville fractional derivative in general Banach spaces in the present paper. First we derive the uniqueness and existence of mild solutions for functional differential equations by the approach of fixed point and fractional resolvent under more general settings. Then we present new sufficient conditions for approximate controllability of functional control system by means of the iterative and approximate method. Our results unify and generalize some previous works on this topic.