Existence and uniqueness of mild solutions for semilinear integro-differential equations of fractional order with nonlocal initial conditions and delays

In this paper, we establish the existence and uniqueness of mild solutions for a class of semilinear integro-differential equations of fractional order with nonlocal initial conditions and delays in á-norm. And the main tool is the fixed point theorem due to Sadovskii. Some known results are generalized.