Combined Delta-Nabla Sum Operator in Discrete Fractional Calculus

Abstract

We introduce a more general discrete fractional operator, given by convex linear combination of the delta and nabla fractional sums. Fundamental properties of the new fractional operator are proved. As particular cases, results on delta and nabla discrete fractional calculus are obtained.

This is a preprint of a paper whose final form has appeared in Commun. Frac. Calc. 1 (2010) 41-47

References in corpus (4)

• Discrete-Time Fractional Variational Problems
• Diamond-$\alpha$ Jensen's Inequality on Time Scales
• The diamond-alpha Riemann integral and mean value theorems on time scales
• A Study of Diamond-alpha dynamic equations on regular time scales