Existence results for some fractional differential equations with nonlocal conditions

Abstract

We are concerned in this paper with the existence results of the Cauchy problem for the fractional differential equation with non local conditions in $\R^n$: $$D^{q}x(t) = Ax(t)+f(t,x(t)),\quad t\in [0,T],\quad x(0)+g(x) = x_0$$ where $0<q<1$.