Symmetric Differentiation on Time Scales

Abstract

We define a symmetric derivative on an arbitrary nonempty closed subset of the real numbers and derive some of its properties. It is shown that real-valued functions defined on time scales that are neither delta nor nabla differentiable can be symmetric differentiable.

This is a preprint of a paper whose final and definite form will be published in Applied Mathematics Letters. Submitted 30-Jul-2012; revised 07-Sept-2012; accepted 10-Sept-2012

Cited by in corpus (2)

• A Fractional Calculus on Arbitrary Time Scales: Fractional Differentiation and Fractional Integration
• Time Scale Version of the Hermite--Hadamard Inequality for Functions Convex on the Coordinates