Symmetric duality for left and right Riemann-Liouville and Caputo fractional differences

Abstract

A discrete version of the symmetric duality of Caputo-Torres, to relate left and right Riemann-Liouville and Caputo fractional differences, is considered. As a corollary, we provide an evidence to the fact that in case of right fractional differences, one has to mix between nabla and delta operators. As an application, we derive right fractional summation by parts formulas and left fractional difference Euler-Lagrange equations for discrete fractional variational problems whose Lagrangians depend on right fractional differences.

This is a preprint of a paper whose final and definite form is published open access in the 'Arab Journal of Mathematical Sciences' (ISSN: 1319-5166), available at [http://dx.doi.org/10.1016/j.ajmsc.2016.07.001]

References in corpus (5)

• Discrete-Time Fractional Variational Problems
• Fractional $h$-difference equations arising from the calculus of variations
• Necessary Optimality Conditions for Fractional Difference Problems of the Calculus of Variations
• A Fractional Calculus on Arbitrary Time Scales: Fractional Differentiation and Fractional Integration
• Duality for the left and right fractional derivatives

Cited by in corpus (2)

• Solutions of systems with the Caputo-Fabrizio fractional delta derivative on time scales
• Time-Fractional Optimal Control of Initial Value Problems on Time Scales