Advances in Difference Equations
Volume 2010 (2010), Article ID 287861, 9 pages
doi:10.1155/2010/287861
Research Article

Mild Solutions for Fractional Differential Equations with Nonlocal Conditions

Fang Li

School of Mathematics, Yunnan Normal University, Kunming 650092, China

Received 8 January 2010; Accepted 21 January 2010

Academic Editor: Gaston Mandata N'Guerekata

Copyright © 2010 Fang Li. 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 mild solution of the fractional differential equations with nonlocal conditions dqx(t)/dtq=−Ax(t)+f(t,x(t),Gx(t)),  t∈[0,T],   and  x(0)+g(x)=x0, in a Banach space X, where 0<q<1. General existence and uniqueness theorem, which extends many previous results, are given.