Abstract:
In this paper, we define left and right Caputo fractional sums and differences, study some of their properties and then relate them to Riemann-Liouville ones studied before by Miller K. S. and Ross B., Atici F.M. and Eloe P. W., Abdeljawad T. and Baleanu D., and a few others. Also, the discrete version of the Q-operator is used to relate the left and right Caputo fractional differences. A Caputo fractional difference equation is solved. The solution proposes discrete versions of Mittag-Leffler functions