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. | |