Local Stability Framework for Caputo Fractional Derivative

In this thesis a local stability theory framework is proposed for Caputo dynamical systems. It is shown that under suitable conditions that a hyperbolic equilibrium point is a stable spiral or unstable spiral. In addition, we provide new results for the non-hyperbolic equilibrium point for a Caputo dynamical system. Specifically, it is shown that, under suitable conditions, the non-hyperbolic equilibrium point of a Caputo dynamical system is locally asymptotically stable.