Generalized Mittag–Leffler Stability of Hilfer Fractional Order Nonlinear Dynamic System

Abstract

This article studies the generalized Mittag−Leffler stability of Hilfer fractional nonautonomous system by using the Lyapunov direct method. A new Hilfer type fractional comparison principle is also proved. The novelty of this article is the fractional Lyapunov direct method combined with the Hilfer type fractional comparison principle. Finally, our main results are explained by some examples.

Keywords

• generalized Mittag–Leffler stability
• Hilfer fractional nonautonomous system
• Hilfer type fractional comparison principle
• fractional Lyapunov direct method