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

Abstract

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.

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