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Fractional h-difference equations arising from the calculus of variations

Ferreira Rui A.C. (Department of Mathematics, Faculty of Engineering and Natural Sciences, Lusophone University of Humanities and Technologies, Lisbon, Portugal)
Torres Delfim F.M. (Department of Mathematics, University of Aveiro, Aveiro, Portugal)

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.

Keywords: Fractional discrete calculus, fractional difference calculus of variations, Euler-Lagrange equations, explicit solutions