  The recent theory of fractional $h$-difference equations introduced in [N. R.
O. Bastos, R. A. C. Ferreira, D. F. M. Torres: Discrete-time fractional
variational problems, Signal Process. 91 (2011), no. 3, 513--524], is enriched
with useful tools for the explicit solution of discrete equations involving
left and right fractional difference operators. New results for the right
fractional $h$ sum are proved. Illustrative examples show the effectiveness of
the obtained results in solving fractional discrete Euler-Lagrange equations.
