  This paper investigates the global stability and the global asymptotic
stability independent of the sizes of the delays of linear time-varying Caputo
fractional dynamic systems of real fractional order possessing internal point
delays. The investigation is performed via fixed point theory in a complete
metric space by defining appropriate non-expansive or contractive self-
mappings from initial conditions to points of the state- trajectory solution.
The existence of a unique fixed point leading to a globally asymptotically
stable equilibrium point is investigated in particular under easily testable
sufficiency-type stability conditions. The study is performed for both the
uncontrolled case and the controlled case under a wide class of state feedback
laws.
