  In fractional calculus there are two approaches to obtain fractional
derivatives. The first approach is by iterating the integral and then defining
a fractional order by using Cauchy formula to obtain Riemann fractional
integrals and derivatives. The second approach is by iterating the derivative
and then defining a fractional order by making use of the binomial theorem to
obtain Gr\"{u}nwald-Litnikov fractional derivatives. In this article we
formulate the delta and nabla discrete versions for left and right fractional
integrals and derivatives representing the second approach. Then, we use the
discrete version of the Q-operator and some discrete fractional dual identities
to prove that the presented fractional differences and sums coincide with the
discrete Riemann ones describing the first approach.
