REFERENCES
[1] A. Kilbas, H. Srivastava, J. Trujillo, Theory and applications of fractional differential equations. Elsevier, 2016.
[2] I. Podlubny, Fractional Differential Equations. Mathematics in Sciences and Engineering, Academic Press, San Diego, 1999.
[3] T. Kaczorek, Selected Problems of Fractional Systems Theory. Springer-Verlag, Berlin, Heidelberg, 2011.
[4] K. S. Miller, B. Ross, Fractional difference calculus. In: Proc. International Symposium on Univalent Functions, Fractional Calculus and their Applications, Nihon University, Koriyama 1988, pp. 139-152.
[5] D. Mozyrska, E. Girejko, Overview of fractional h-difference operators. In: Advances in Harmonic Analysis and Operator Theory: The Stefan Samko Anniversary Volume (A. Almeida, L. Castro, F. O. Speak, eds.), Operator Theory: Advances and Applications, Springer 2013, pp. 253-268. DOI:10.1007/978-3-0348-0516-2_14
[6] M. Wyrwas, E. Girejko, D. Mozyrska, E. Pawluszewicz, Stability of fractional difference systems with two orders. In: Advances in the Theory and Applications of Non-integer Order Systems (W. Mitkowski, J. Kacprzyk, and J. Baranowski, eds.), Lect. Notes Electr. Engrg. 257, Springer International Publishing, Switzerland 2013, pp. 41-52. DOI:10.1007/978-3-319-00933-9_4
[7] B. G. Jia, X. Liu, F. F. Du, M.Wang, The solution of a new Caputo-like fractional h-difference equation, Rocky Mountain J. Math. 2017, to appear.
[8] M. Wyrwas, E. Pawluszewicz, E. Girejko, Stability of nolinear h-difference systems with n fractional orders. Kybernetika, 51 (1) (2015), 112-136.
[9] D. Mozyrska, E. Girejko, M. Wyrwas, Comparison of h-difference fractional operators. In: Advances in the Theory and Applications of Non-integer Order Systems (W. Mitkowski, J. Kacprzyk, and J. Baranowski, eds.), Lect. Notes Electr. Engrg. 257, Springer International Publishing, Switzerland 2013, pp. 191-197. DOI:10.1007/978-3-319-00933-9_17
[10] N. R. O. Bastos, R. A. C. Ferreira, D. F. M. Torres, Discrete time fractional variational problems, Signal Processing, 91 (2011), 513-524. DOI: 10.1016/j.sigpro.201 0.05.001
[11] D. Mozyrska, M. Wyrwas, The Z-transform method and delta type fractional difference operators. Discret. Dyn. Nat. Soc., 2015 (2015), Article ID 852734, 12 pages.
[12] S.Momani, S. Hadid, Lyapunov stability solutions of fractional integrodifferential equations. Int. J. Math. Math. Sci., 47 (2004), 2503-2507.
[13] L. G. Zhang, J. M. Li, G. P. Chen, Extension of Lyapunov second method by fractional calculus. Pure Appl. Math., 3 (2005), 1008-5513.
[14] V. E. Tarasov, Fractional stability, 2007. Available online: http://arxiv.org/abs/0711.2117v1.
[15] D. Matignon, Stability properties for generalized fractional differential systems. ESAIM Proc., 5 (1998), 145-158.
[16] Y. Li, Y. Q. Chen, I. Podlubny, Mittag-Leffler stability of fractional order nonlinear dynamic systems. Automatica, 45 (2009), 1965-1969. DOI:10.1140/epjst/e20 11-01379-1
[17] Y. Li, Y. Q. chen, I. Podlubny, Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag-Leffler stability. Comput. Math. Appl., 59 (2010), 1810-1821. DOI:10.1016/j.camwa.2009.08.019
[18] J. M. Yu, H. Hu, S. B. Zhou, X. R. Lin, Generalized Mittag-Lefler stability of multi-variables fractional order nonlinear systems. Automatica, 49 (2013), 1798-1803.
[19] F. R. Zhang, C. P. Li, Y. Q. Chen, Asymptotical stability of nolinear fractional differential systems with Caputo derivative. Internat. J. Differ. Equ., Volume 2011, Article ID 635165, 12 pages.
[20] M. Wyrwas, D. Mozyrska, On Mittag-Leffler stability of fractional order difference systems. In: Advances in Modeling and Control of Non-integer order systems, (K. J. Latawiec et al. eds.), Lect. Notes Electr. Engrg. 320, Springer International Publishing, Switzerland 2015, pp. 209-220. DOI:10.1007/978-3-319-09900-2_19
[21] F. Jarad, T. Abdeljawad, D. Baleanu, K. Bi¸cen, On the stability of some discrete fractional nonautonomous systems. Abstr. Appl. Anal., Volume 2012, Article ID 476581, 9 pages. doi:10.1155/2012/476581