Mild Solutions for Fractional Differential Equations with Nonlocal Conditions

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.