摘要：In this paper, we introduce the analogue of Caputo type fractional derivatives on a ( q , h ) $(q,h)$ -discrete time scale which can be reduced to Caputo type fractional differences studied by Abdeljawad (Comput. Math. Appl. 62:1602-1611, 2011) and Caputo type fractional q-differences studied by Atici and Eloe via the choice q = h = 1 $q=h=1$ and h = 0 $h=0$ , respectively. Then, we solve linear fractional difference equations involving Caputo type ( q , h ) $(q,h)$ -derivatives and give the general solutions in terms of discrete Mittag-Leffler functions introduced by Cermak et al. In addition, we also apply the ( q , h ) $(q,h)$ -Laplace transform method to solve these linear fractional order difference equations.
