Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 275, pp. 1-21.

Title: Approximate controllability of abstract  impulsive fractional
       neutral evolution equations with infinite delay in Banach spaces

Authors: Dimplekumar N. Chalishajar (Virginia Military Institute, Lexington, VA, USA)
         Kandasamy Malar (Erode Arts and Science College, Erode, India)
         Kulandhivel Karthikeyan (K.S.R. College of Technology, Tamil Nadu,  India)

Abstract:
 In this  article, we study  the approximate controllability of impulsive
 abstract fractional neutral evolution equations in Banach spaces.
 The main results are obtained by using Krasnoselkii's fixed point theorem,
 fractional calculus and methods of controllability theory. An application
 is provided to illustrate the theory. Here we have provided new definition
 of phase space for the impulsive and infinite delay term. Our result is
 new for the approximate controllability with infinite delay in Hilbert space.

Submitted July 26, 2013. Published December 18, 2013.
Math Subject Classifications: 34A37, 34K30, 47D09, 93C15.
Key Words: Impulsive conditions; approximate controllability;
           neutral evolution equations; phase space.