On explicit stability conditions for a linear fractional difference system
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T. Abdeljawad, On Riemann and Caputo fractional differences. Comput. Math. Appl. 62, No 3 (2011), 1602–1611.
R. Abu-Saris, Q. Al-Mdallal, On the asymptotic stability of linear system of fractional-order difference equations. Fract. Calc. Appl. Anal. 16, No 3 (2013), 613–629; DOI: 10.2478/s13540-013-0039-2; http://www.degruyter.com/view/j/fca.2013.16.issue-3/s13540-013-0039-2/s13540-013-0039-2.xml; http://link.springer.com/article/10.2478/s13540-013-0039-2.
J.A.D. Appleby, I. Gyori, D.W. Reynolds, On exact convergence rates for solutions of linear systems of Volterra difference equations. J. Differ. Equ. Appl. 12, No 12 (2006), 1257–1275.
T.M. Apostol, Mathematical Analysis. 2nd Ed., World Student Series Edition, Addison-Wesley (1974).
F.M. Atici, P.W. Eloe, A transform method in discrete fractional calculus. Int. J. Differ. Equ. 2, No 2 (2007), 165–176.
F.M. Atici, P.W. Eloe, Linear systems of fractional nabla difference equations. Rocky Mt. J. Math. 41, No 2 (2011), 353–370.
F. Chen, Fixed points and asymptotic stability of nonlinear fractional difference equations. El. J. Qualit. Theory Differ. Equ. 2011, No 39 (2011), 18 pages.
J. Čermák, T. Kisela, L. Nechvátal, Stability regions for linear fractional differential systems and their discretizations. Appl. Math. Comput. 219, No 12 (2013), 7012–7022.
J. Čermák, L. Nechvátal, On (q, h)-analogue of fractional calculus, J. Nonlinear Math. Phys. 17, No 1 (2010), 51–68.
S. Elaydi, An Introduction to Difference Equations. 3rd Ed., Undergraduate Texts in Mathematics, Springer, New York (2005).
S. Elaydi, S. Murakami, Asymptotic stability versus exponential stability in linear Volterra difference equations of convolution type. J. Differ. Equ. Appl. 2, No 4 (1996), 401–410.
R.A.C. Ferreira, D.F.M. Torres, Fractional h-difference equations arising from the calculus of variations. Appl. Anal. Discrete Math. 5, No 1 (2011), 110–121.
L. Galeone, R. Garrappa, On multistep methods for differential equations of fractional order. Mediterr. J. Math. 3, No 3 (2006), 565–580.
L. Galeone, R. Garrappa, Explicit methods for fractional differential equations and their stability properties. J. Comput. Appl. Math. 228, No 2 (2009), 548–560.
T. Kisela, An analysis of the stability boundary for a linear fractional difference system. Math. Bohem. (to appear).
C.P. Li, Y. Ma, Fractional dynamical system and its linearization theorem. Nonlinear Dyn. 71, No 4 (2013), 621–633
C.P. Li, F.R. Zhang, A survey on the stability of fractional differential equations. Eur. Phys. J. Spec. Top. 193, No 1 (2011), 27–47.
C. Lubich, A stability analysis of convolution quadratures for Abel- Volterra integral equations. IMA J. Numer. Anal. 6, No 1 (1986), 87–101.
D. Matignon, Stability results for fractional differential equations with applications to control processing. In: Computational Engineering in Systems and Application Multiconference, IMACS, IEEE-SMC, Lille, France, Vol. 2 (1996), 963–968.
I. Petráš, Stability of fractional-order systems with rational orders: a survey. Fract. Calc. Appl. Anal. 12, No 3 (2009), 269–298; available at http://www.math.bas.bg/∼fcaa.
I. Petráš, Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation. Higher Education Press, Springer, Beijing, Berlin (2011).
I. Podlubný, Fractional Differential Equations. Academic Press, New Jersey (1999).