Initial Time Difference Strict Stability of Fractional Dynamic Systems

2011 ◽  
pp. 133-144
Author(s):  
Coşkun Yakar ◽  
Mustafa Bayram Gücen
Keyword(s):  
Dynamic Systems ◽  
Time Difference ◽  
Initial Time ◽  
Strict Stability

Strict stability with respect to initial time difference for Caputo fractional differential equations by Lyapunov functions

2017 ◽  
Vol 24 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Ravi P. Agarwal ◽  
Donal O’Regan ◽  
Snezhana Hristova
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Time Difference ◽  
Initial Time ◽  
Advantages And Disadvantages ◽  
Strict Stability ◽  
Caputo Fractional Differential Equations ◽  
Fractional Differential

AbstractThe strict stability properties are generalized to nonlinear Caputo fractional differential equations in the case when both initial points and initial times are changeable. Using Lyapunov functions, some criteria for strict stability, eventually strict stability and strict practical stability are obtained. A brief overview of different types of derivatives in the literature related to the application of Lyapunov functions to Caputo fractional equations are given, and their advantages and disadvantages are discussed with several examples. The Caputo fractional Dini derivative with respect to to initial time difference is used to obtain some sufficient conditions.

scholarly journals Initial Time Difference Stability of Causal Differential Systems in terms of Lyapunov Functions and Lyapunov Functionals

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Coşkun Yakar ◽  
Mustafa Bayram Gücen
Keyword(s):  
Differential System ◽  
Lyapunov Functions ◽  
Lyapunov Functional ◽  
Initial Position ◽  
Time Difference ◽  
Initial Time ◽  
Qualitative Behavior ◽  
Lyapunov Functionals ◽  
Comparison Result ◽  
Differential Systems

We investigate the qualitative behavior of a perturbed causal differential equation that differs in initial position and initial time with respect to the unperturbed causal differential equations. We compare the classical notion of stability of the causal differential systems to the notion of initial time difference stability of causal differential systems and present a comparison result in terms of Lyapunov functions. We have utilized Lyapunov functions and Lyapunov functional in the study of stability theory of causal differential systems when establishing initial time difference stability of the perturbed causal differential system with respect to the unperturbed causal differential system.

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