Chapter 7: Stability of a Class of Discrete Fractional Nonautonomous Systems

We notice that the discrete fractional calculus is a new concept suggested in [Miller and Ross (1989)]. Since that pioneering work several results were reported on this subject (see for example [Atici and Eloe (2007, 2009a,b); Abdeljawad and Baleanu (2011a); Abdeljawad (2011); Jarad et al. (2012); Baleanu et al. (2006); Abdeljawad et al. (2013); Abdeljawad and Baleanu (2011b)] and the references therein). This new concept describes better in some cases the dynamics of complex or hypercomplex systems. Some of the recent reported applications can be see in [Wu and Baleanu (2014a); Wu et al. (2014); Wu and Baleanu (2014b)]. One of the key concept in this new field is the stability of fractional-order dynamic systems which was already investigated in [Chen et al. (1995); Lazarevic (2006); Deng et al. (2007); Merrikh-Bayat and Karimi-Ghartemani (2009); Zhang (2008); Momani and Hadid (2004); Li et al. (2010); Jarad et al. (2012)] and the references therein, while the stability of discrete dynamic systems was a the subject of many books and articles such as [Agarwal (2000)] and the references therein.