scholarly journals Uniqueness and Novel Finite-Time Stability of Solutions for a Class of Nonlinear Fractional Delay Difference Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Danfeng Luo ◽  
Zhiguo Luo

This paper focuses on the uniqueness and novel finite-time stability of solutions for a kind of fractional-order nonlinear difference equations with time-varying delays. Under some new criteria and by applying the generalized Gronwall inequality, the new constructive results have been established in the literature. As an application, two typical examples are delineated to demonstrate the effectiveness of our theoretical results.

2020 ◽  
Vol 34 (30) ◽  
pp. 2050341
Author(s):  
Ruiyang Qiu ◽  
Ruihai Li

In this paper, a spring-mass system with impacts and frictions is formulated by the impulsive differential system. An energy-like Lyapunov function and an auxiliary step function are constructed to analyze the finite-time stability of such impact system with a time-varying external force and sliding friction as well as air resistance. We establish the sufficient conditions of finite-time stability for three cases of the spring-mass system, and present numerical simulations for each case to verify the validity of the theoretical results.


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