Discrete conditions of Lyapunov stability

Stieltjes动力系统解的可延拓性与Lyapunov稳定性

Prolongation of solutions and Lyapunov stability for Stieltjes dynamical systems

本文针对Stieltjes动力系统，利用解延拓结果证明最大解全局存在，并通过Lyapunov第二方法建立一致稳定性与一致渐近稳定性判据，最后应用于两个种群动力学模型。

Lyapunov type inequality for discrete fractional boundary value problem

In this paper, we obtain Lyapunov type inequality for discrete fractional boundary value problem.

Stability of fractional-order nonlinear systems by Lyapunov direct method

In this paper, by using a characterization of functions having fractional derivative, we propose a rigorous fractional Lyapunov function candidate method to analyze stability of fractional-order nonlinear systems. First, we prove an inequality concerning the fractional derivatives of convex Lyapunov functions without the assumption on the existence of derivative of pseudo-states. Second, we establish fractional Lyapunov functions to fractional-order systems without the assumption on the global existence of solutions. Our theorems fill the gaps and strengthen results in some existing papers.

Lyapunov-Type Inequalities for Discrete Riemann-Liouville Fractional Boundary Value Problems

In this article we establish a few Lyapunov-type inequalities for two-point discrete fractional boundary value problems involving Riemann-Liouville type backward differences. To illustrate the applicability of established results, we obtain criteria for the nonexistence of nontrivial solutions and estimate lower bounds for eigenvalues of the corresponding eigenvalue problems. We also apply these inequalities to deduce criteria for the nonexistence of real zeros of certain discrete Mittag-Leffler functions.

Stability by Lyapunov functions of Caputo fractional differential equations with non-instantaneous impulses

The stability of the zero solution of a nonlinear Caputo fractional differential equation with noninstantaneous impulses is studied using Lyapunov like functions. The novelty of this paper is based on the new definition of the derivative of a Lyapunov like function along the given noninstantaneous impulsive fractional differential equations. On one side this definition is a natural generalization of Caputo fractional Dini derivative of a function and on the other side it allows us the assumption for Lyapunov functions to be weakened to continuity. By appropriate examples it is shown the natura…

Existence of positive solutions to a discrete fractional boundary value problem and corresponding Lyapunov-type inequalities

We prove existence of positive solutions to a boundary value problem depending on discrete fractional operators. Then, corresponding discrete fractional Lyapunov-type inequalities are obtained.