Inspired by the results of F. M. Atici
and P. W. Eloe
[Int. J. Difference Equ. 2, No. 2, 165–176 (2007), Proc. Am. Math. Soc. 137, No. 3, 981–989 (2009; Zbl 1166.39005
)] and K. S. Miller
and B. Ross
[An introduction to the fractional calculus and fractional differential equations. New York: John Wiley & Sons (1993; Zbl 0789.26002
)], the authors introduce right fractional sum and difference operators. Based upon the provided theory, a by-part formula is given analogous to the one in usual fractional calculus. Towards the end of the paper, the obtained results are implemented to derive Euler-Lagrange equations for a discrete variational problem in fractional calculus.