J. Nonl. Evol. Equ. Appl. 2014 (2), pp. 13-28, published on December 10, 2014:

Existence of a solution for history valued neutral fractional differential equation with a nonlocal condition

A. Chadha, D. N. Pandey

Department of Mathematics, Indian Institute of Technology Roorkee
Roorkee, Uttarakhand, India, Pin-247667

Received on October 14, 2013, Revised version April 23, 2014
Accepted on April 24, 2014

Communicated by Gaston M. N'Guérékata

Abstract.  In this present work, we study the existence of mild solutions of historyvalued neutral delay differential equation of fractional order with nonlocal condition in a Banach space X. The existence of mild solutions is established by using a resolvent operator and fixed point theorem.
Keywords:Fractional calculus, Caputo derivative, Nonlocal condition, Resolvent operator, Neutral fractional differential equation.
2010 Mathematics Subject Classification:   34K37, 34K30, 35R11, 47N20.

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