Abstract
Abstract The logarithmic time evolution is widely observed in laboratory and field measurements. However, logarithmic stability has not been well considered till now. In this paper, the definition of Lyapunov stability, including logarithmic and inverse Mittag-Leffler stabilities, is proposed. And via the Lyapunov direct method, the stability of nonlinear dynamical systems based on the structural derivative is investigated. Furthermore, the comparison principle based on the structural derivative is presented in order to obtain the stability conditions for nonlinear dynamical systems. Finally, two demonstrative examples are given to test the proposed stability concept.
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