Electron. J. Diff. Equ., Vol. 2013 (2013), No. 275, pp. 1-21.

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

Dimplekumar N. Chalishajar, Kandasamy Malar, Kulandhivel Karthikeyan

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.

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Dimplekumar N. Chalishajar
Department of Mathematics and Computer Science
Virginia Military Institute (VMI)
417, Mallory Hall, Lexington, VA 24450, USA
email: dipu17370@yahoo.com, chalishajardn@vmi.edu
Kandasamy Malar
Department of Mathematics, Erode Arts and Science College
Erode 638 009, Tamil Nadu. India
email: malarganesaneac@gmail.com
Kulandhivel Karthikeyan
Department of Mathematics, K.S.R. College of Technology
Tiruchengode 637 215, Tamil Nadu, India
email: karthi_phd2010@yahoo.co.in

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