Fractional differential equations in terms of comparison results and Lyapunov stability with initial time difference.
Yakar, Coşkun (2010)
Abstract and Applied Analysis
Similarity:
Displaying similar documents to “Stability of Caputo fractional differential equations by Lyapunov functions”
Fractional differential equations in terms of comparison results and Lyapunov stability with initial time difference.
An analysis of the stability boundary for a linear fractional difference system
Tomáš Kisela (2015)
Mathematica Bohemica
Similarity:
This paper deals with basic stability properties of a two-term linear autonomous fractional difference system involving the Riemann-Liouville difference. In particular, we focus on the case when eigenvalues of the system matrix lie on a boundary curve separating asymptotic stability and unstability regions. This issue was posed as an open problem in the paper J. Čermák, T. Kisela, and L. Nechvátal (2013). Thus, the paper completes the stability analysis of the corresponding fractional...
Stability analysis of fractional differential systems with order lying in .
Zhang, Fengrong, Li, Changpin (2011)
Advances in Difference Equations [electronic only]
Similarity:
Fractional descriptor continuous-time linear systems described by the Caputo-Fabrizio derivative
Tadeusz Kaczorek, Kamil Borawski (2016)
International Journal of Applied Mathematics and Computer Science
Similarity:
The Weierstrass-Kronecker theorem on the decomposition of the regular pencil is extended to fractional descriptor continuous-time linear systems described by the Caputo-Fabrizio derivative. A method for computing solutions of continuous-time systems is presented. Necessary and sufficient conditions for the positivity and stability of these systems are established. The discussion is illustrated with a numerical example.
Razumikhin stability theorem for fractional systems with delay.
Baleanu, D., Sadati, S.J., Ghaderi, R., Ranjbar, A., Abdeljawad, T., Jarad, F. (2010)
Abstract and Applied Analysis
Similarity:
Equivalent descriptions of a discrete-time fractional-order linear system and its stability domains
Piotr Ostalczyk (2012)
International Journal of Applied Mathematics and Computer Science
Similarity:
Two description forms of a linear fractional-order discrete system are considered. The first one is by a fractional-order difference equation, whereas the second by a fractional-order state-space equation. In relation to the two above-mentioned description forms, stability domains are evaluated. Several simulations of stable, marginally stable and unstable unit step responses of fractional-order systems due to different values of system parameters are presented.
Simple conditions for practical stability of positive fractional discrete-time linear systems
Mikołaj Busłowicz, Tadeusz Kaczorek (2009)
International Journal of Applied Mathematics and Computer Science
Similarity:
In the paper the problem of practical stability of linear positive discrete-time systems of fractional order is addressed. New simple necessary and sufficient conditions for practical stability and for practical stability independent of the length of practical implementation are established. It is shown that practical stability of the system is equivalent to asymptotic stability of the corresponding standard positive discrete-time systems of the same order. The discussion is illustrated...
Exact solution of impulse response to a class of fractional oscillators and its stability.
Li, Ming, Lim, S.C., Chen, Shengyong (2011)
Mathematical Problems in Engineering
Similarity:
New existence and stability results for partial fractional differential inclusions with multiple delay
Saïd Abbas, Wafaa A. Albarakati, Mouffak Benchohra, Mohamed Abdalla Darwish, Eman M. Hilal (2015)
Annales Polonici Mathematici
Similarity:
We discuss the existence of solutions and Ulam's type stability concepts for a class of partial functional fractional differential inclusions with noninstantaneous impulses and a nonconvex valued right hand side in Banach spaces. An example is provided to illustrate our results.