Fractional $h$-difference equations arising from the calculus of variations

Details Fractional $h$-difference equations arising from the calculus of variations Fractional $h$-difference equations arising from the calculus of variations

2011-01-31

arxiv.org/abs/1101.5904v1

Appl. Anal. Discrete Math., Vol. 5 (2011), no. 1, 110--121

Mathematics

Classical Analysis and ODEs

Submitted 15-Aug-2010; revised 16-Jan-2011 and 30-Jan-2011; accepted 31-Jan-2011; for publication in Applicable Analysis and D

Scientific paper

10.2298/AADM110131002F

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.

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