Nonlocal stochastic differential equations with time‐varying delay driven by G ‐Brownian motion

2019 ◽  
Vol 43 (2) ◽  
pp. 600-612 ◽  
Author(s):  
Wensheng Yin ◽  
Jinde Cao
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Time Varying ◽  
Time Varying Delay ◽  
Varying Delay

New finite-time stability analysis of singular fractional differential equations with time-varying delay

2020 ◽  
Vol 23 (2) ◽  
pp. 504-519 ◽  
Author(s):  
Nguyen T. Thanh ◽  
Vu N. Phat ◽  
Piyapong Niamsup
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Finite Time ◽  
Time Varying ◽  
Time Stability ◽  
Finite Time Stability ◽  
Time Varying Delay ◽  
Singular Fractional Differential Equations ◽  
Fractional Differential ◽  
Varying Delay

AbstractThe Lyapunov function method is a powerful tool to stability analysis of functional differential equations. However, this method is not effectively applied for fractional differential equations with delay, since the constructing Lyapunov-Krasovskii function and calculating its fractional derivative are still difficult. In this paper, to overcome this difficulty we propose an analytical approach, which is based on the Laplace transform and “inf-sup” method, to study finite-time stability of singular fractional differential equations with interval time-varying delay. Based on the proposed approach, new delay-dependent sufficient conditions such that the system is regular, impulse-free and finite-time stable are developed in terms of a tractable linear matrix inequality and the Mittag-Leffler function. A numerical example is given to illustrate the application of the proposed stability conditions.

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