REFERENCES
[1] R.P. Agarwal, Difference Equations and Inequalities, Marcel Dekker, New York, 1992.
[2] Baoguo Jia, Lynn Erbe, and Allan Peterson, Comparison theorems and asymptotic behaviour of solutions of discrete fractional equations, Electronic Journal of Qualitative Theory of Differential Equations, 89 (2015),1-18.
[3] Christopher Goodrich and Allan C. Peterson, Discrete Fractional Calculus, Springer International Publishing, 2015, doi: 10.1007/978-3-319-25562-0.
[4] S. Elaydi, An Introduction to Difference Equations, Third Edition, Springer, New York, 2005.
[5] Ferhan M. Atici and Paul W. Eloe, Linear systems of nabla fractional difference equations, Rocky Mountain Journal of Mathematics, 41, No. 2 (2011), 353-370.
[6] H. L. Gray, N.F. Zhang, On a new definition of the fractional difference, Mathematics of Computation, 50, No. 182 (1988), 513-529.
[7] R.A. Horn and C.R. Johnson, Matrix Analysis, Cambridge University Press, New York, 1985.
[8] Jan Cermak, Tomas Kisela and Ludek Nechvatal, Stability and asymptotic properties of a linear fractional difference equation, Advances in Difference Equations (2012), 122.
[9] Jan Cermak, Istvan Gyori and Ludek Nechvatal, Stability regions for linear fractional difference systems and their discretizations, Applied Mathematics and Computation, 219 (2013), 7012-7022.
[10] W.G. Kelly, A.C. Peterson, Difference Equations: An Introduction with Applications, Second Edition, Academic Press, San Diego, 1991.
[11] K.S. Miller, B. Ross, Fractional Difference Calculus, Proceedings of the International Symposium on Univalent Functions, Fractional Calculus and Their Applications, 139 - 152, Nihon University, Koriyama, Japan, 1989.
[12] Nihan Acar and Ferhan M. Atici, Exponential functions of discrete fractional calculus, Appl. Anal. Discrete Math., 7 (2013), 343-353.
[13] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.