Existence and uniqueness of solutions to fractional semilinear mixed Volterra-Fredholm integrodifferential equations with nonlocal conditions

In this article we study the fractional semilinear mixed Volterra-Fredholm integrodifferential equation $$ frac{d^{alpha }x(t)}{dt^{alpha }} =Ax(t)+fBig(t,x(t), int_{t_0}^tk(t,s,x(s))ds,int_{t_0}^{T}h(t,s,x(s))dsBig) , $$ where $tin [t_0,T]$, $t_0geq 0$, $0