International Journal of Differential Equations
Volume 2011 (2011), Article ID 793023, 20 pages
http://dx.doi.org/10.1155/2011/793023
Research Article

Existence of the Mild Solutions for Impulsive Fractional Equations with Infinite Delay

Jaydev Dabas,1 Archana Chauhan,2 and Mukesh Kumar2

1Department of Paper Technology, IIT Roorkee, Saharanpur Campus, Saharanpur 247001, India
2Department of Mathematics, Motilal Nehru National Institute of Technology, Allahabad 211 004, India

Received 25 May 2011; Revised 22 July 2011; Accepted 6 August 2011

Academic Editor: D. D. Ganji

Copyright © 2011 Jaydev Dabas et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper is concerned with the existence and uniqueness of a mild solution of a semilinear fractional-order functional evolution differential equation with the infinite delay and impulsive effects. The existence and uniqueness of a mild solution is established using a solution operator and the classical fixed-point theorems.