  We study the existence and approximate controllability of a class of
fractional nonlocal delay semilinear differential systems in a Hilbert space.
The results are obtained by using semigroup theory, fractional calculus, and
Schauder's fixed point theorem. Multi-delay controls and a fractional nonlocal
condition are introduced. Furthermore, we present an appropriate set of
sufficient conditions for the considered fractional nonlocal multi-delay
control system to be approximately controllable. An example to illustrate the
abstract results is given.
