A Cauchy problem for some fractional abstract differential equation with non local conditions (Q1001858)

The author discusses the existence and uniqueness of a solution to the Cauchy problem for the fractional differential equation with non local conditions \[ D^q x(t)=f(t,x(t)),\quad t\in [0,T],\quad x(0)+g(x)=x_0, \] where \(0<q<1\) in a Banach space. Here, the fractional derivative is in the sense of Caputo.