Stretched exponential stability of nonlinear Hausdorff dynamical systems

This paper proposes the definition of stretched exponential stability. First, a non-Debye decay is found in the nonlinear Hausdorff dynamical systems by using the Lyapunov direct method, which leads to the stretched exponential stability. It is worthy of noting that the classical exponential stability is a special case of the proposed stretched exponential stability, when the stretched parameter is in its limiting case equal to 1. Therefore the stretched exponential has more flexibility and applicability to the real-world problems than the classical exponential stability. Second, a fractal comparison principle is applied to obtain stability criteria for the proposed systems. Examples are presented to illustrate the applicability of the proposed concept.