ABSTRACT
This chapter offers stability and boundedness results for fractional order systems using the Lyapunov direct method. It considers sufficient conditions for Lyapunov stability of solutions for different classes of fractional differential equations. The chapter offers boundedness theorems for fractional functional differential equations. The chapter utilizes scalar Lyapunov functions and investigates global stability of the solutions of impulsive fractional differential systems. It continues to use the Lyapunov fractional method, and analyze Mittag–Leffler stability properties of functional and impulsive fractional-order differential equations. The chapter deals with sufficient conditions for practical stability of nonlinear differential systems of fractional order subject to impulse effects. It discusses the Lipschitz stability of fractional functional differential systems with Caputo fractional derivatives. The chapter results on stability and boundedness of the solutions with respect to sets will be given for fractional impulsive functional differential systems using piecewise continuous vector Lyapunov functions and the fractional vector comparison principle.
