On Riemann and Caputo fractional differences

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., Atıcı 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.