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

TL;DR

This paper advances the theory of fractional $h$-difference equations by providing new tools and results for solving fractional discrete Euler-Lagrange equations, enhancing the analytical methods in discrete fractional calculus.

Contribution

It introduces new results for the right fractional $h$ sum and offers explicit solution techniques for fractional difference equations in the calculus of variations.

Findings

New results for the right fractional $h$ sum

Effective solution methods for fractional discrete Euler-Lagrange equations

Illustrative examples demonstrating the methods' effectiveness

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.