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Zbl 1225.39008
Abdeljawad, Thabet; Baleanu, Dumitru
Fractional differences and integration by parts. (English)
[J] J. Comput. Anal. Appl. 13, No. 3, 574-582 (2011). ISSN 1521-1398; ISSN 1572-9206/e

Inspired by the results of {\it F. M. Atici} and {\it 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 {\it K. S. Miller} and {\it 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.
[Murat Adivar (Izmir)]

MSC 2000:: *39A12 Discrete version of topics in analysis
26A33 Fractional derivatives and integrals (real functions)
39A10 Difference equations
49J15 Optimal control problems with ODE (existence)
49M25 Finite difference methods
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

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