A survey on the stability of fractional differential equations

By Changpin Li, F. R. Zhang. 2011

407 citations recorded by the source corpus.

Subfields: Applied Mathematics, Control and Systems Engineering, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/fddfdcf6ba2cd15e529c946ae3f6aeb91a019269

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In Applied Mathematics

In Control and Systems Engineering

In Modeling and Simulation

Citations in the corpus

Stability analysis for nonlinear fractional-order systems based on comparison principle (2014, background): “However, there are few results concerning how to directly analyze and control nonlinear fractionalorder systems except for linearization [30, 31].”
Fractional-order delayed predator–prey systems with Holling type-II functional response (2015, methodology): “In section, we extend the analysis to study the global stability conditions [10,22] for the fractional-order delay differential system.”
HYERS-ULAM-RASSIAS STABILITY OF FRACTIONAL DIFFERENTIAL EQUATION (2015, background): “[16] Li CP, Zhang FR.”
On explicit stability conditions for a linear fractional difference system (2015, background): “Later, many other stability results on fractional differential equations and their systems have appeared (for a basic information we refer to the monographs [23], [24] and the survey papers [17], [21]).”
Stability of Caputo fractional differential equations by Lyapunov functions (2015, methodology): “For fractional differential equations some authors ([3], [10], [12]) defined and used the so called Caputo fractional derivative of Lyapunov functions.”
Linearized Asymptotic Stability for Fractional Differential Equations (2015, background): “There have been many publications on Lypunov’s second method for fractional differential equations and we refer the reader to [7] or [9] for a survey.”
New results on stability and stabilization of a class of nonlinear fractional-order systems (2013, background): “Especially, the development on stability of nonlinear fractional-order equations is a bit slow [16].”
Dissipativity and Stability Analysis for Fractional Functional Differential Equations (2015, background): “For some other progresses, one can see the nice review paper [20] and the valuable new book on the qualitative theory of fractional differential equations [38].”
A survey of Lyapunov functions, stability and impulsive Caputo fractional differential equations (2016, background): “The main condition concerns the Caputo fractional derivative of the Lyapunov function 0 D q tV (t, x(t)), where x(t) is a solution of the studied fractional equation (see, for example, the papers [8], [19], [23], [31], [32]).”