The Lp stability analysis of the basic functions for fractional order systems

In this paper, the L_p stability of the Mittag-Leffler function with two parameters times a power law function t^γ-1E_α,β (-λt^a) is discussed on the infinite time interval. The necessary and sufficient conditions of L_p stability are derived, which show that the discussed function is a continuous intermediate process connecting the exponential, power law and Mittag-Leffler functions. A number of examples about the fractional order Lyapunov method and fractional order systems are illustrated to validate the concepts.