Abdeljawad, Thabet; Baleanu, Dumitru Fractional differences and integration by parts. (English) Zbl 1225.39008 J. Comput. Anal. Appl. 13, No. 3, 574-582 (2011). 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. Reviewer: Murat Adivar (Izmir) Cited in 75 Documents MSC: 39A12 Discrete version of topics in analysis 26A33 Fractional derivatives and integrals 39A10 Additive difference equations 49J15 Existence theories for optimal control problems involving ordinary differential equations 49M25 Discrete approximations in optimal control 39A70 Difference operators Keywords:left fractional sum; right fractional sum; left and right fractional differences; integration by parts; Euler-Lagrange equation; difference operators; fractional calculus; discrete variational problem Citations:Zbl 1166.39005; Zbl 0789.26002 PDFBibTeX XMLCite \textit{T. Abdeljawad} and \textit{D. Baleanu}, J. Comput. Anal. Appl. 13, No. 3, 574--582 (2011; Zbl 1225.39008)