  We study the regional controllability problem for delayed fractional control
systems through the use of the standard Caputo derivative. First, we recall
several fundamental results and introduce the family of fractional-order
systems under consideration. Afterwards, we formulate the notion of regional
controllability for fractional systems with control delays and give some of
their important properties. Our main method consists in defining an attainable
set, which allow us to prove exact and weak controllability. Moreover, main
results include not only those of controllability but also a powerful Hilbert
uniqueness method that allow us to solve the minimum energy optimal control
control problem. Precisely, an explicit control is obtained that drives the
system from an initial given state to a desired regional state with minimum
energy. Examples are given to illustrate the obtained theoretical results.
