2010/10/15 by Manuel De la Sen, M. De La Sen, De La Sen, M.
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Fractional Differential Equations Solutions #Nonlinear Differential Equations Analysis #Numerical methods for differential equations #math.DS
paper · pdf · doi:10.48550/arxiv.1010.3204
arxiv created 2010/10/15 · openalex publication_date 2010/10/15 · arxiv updated 2010/10/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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.