J. Nonl. Evol. Equ. Appl. 2012 (5), pp. 57-67, published on August 26, 2012:

Controllability of impulsive fractional order semilinear evolution equations with nonlocal conditions.

N. K. Tomar

School of Basic Sciences, Indian Institute of Technology Patna, Patna-800 013, Bihar, India

J. Dabas

Department of Paper Technology, Indian Institute of Technology, Roorkee, Saharanpur Campus, Saharanpur-247001,UP, India

Received on October 22, 2011, revised version on March 19, 2011
Accepted on March 20, 2012

Communicated by Gisèle M. Mophou

Abstract.  The controllability problem for a class of impulsivefractional-order semilinear control system with nonlocal initial condition has been considered. Sufficient condition for the controllability is established by means of solution operator and application of Banach contraction theorem.
Keywords: Controllability, Fractional order differential equation, Nonlocal conditions, Contractions, Mild solution, Impulsive conditions.
2010 Mathematics Subject Classification:   93B05, 34K05, 34A12, 34A37, 26A33.

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