Analysis of Caputo linear fractional dynamic systems with time delays through fixed point theory

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.