Author ORCID Identifier

Goodrich - https://orcid.org/0000-0003-2058-216X

Document Type

Article

Publication Date

3-10-2021

Publication Title

Journal of Difference Equations and Applications

Volume

27

Issue

3

First Page

317

Last Page

341

DOI

https://doi.org/10.1080/10236198.2021.1894142

Abstract

We investigate relationships between the sign of the discrete fractional sequential difference (Δv 1+a-μ Δμaf)(t) and the convexity of the function t→f(t). In particular, we consider the case in which the bound (Δv 1+a-μ Δμaf)(t) ≥εf(a), for some ε > 0 and where f(a) < 0 is satisfied. Thus, we allow for the case in which the sequential difference may be negative, and we show that even though the fractional difference can be negative, the convexity of the function f can be implied by the above inequality nonetheless. This demonstrates a significant dissimilarity between the fractional and non-fractional cases. We use a combination of both hard analysis and numerical simulation.

Comments

This is an Accepted Manuscript of an article published by Taylor & Francis in Journal of Difference Equations and Applications on March 10, 2021, available online: https://doi-org.leo.lib.unomaha.edu/10.1080/10236198.2021.1894142

Creative Commons License

Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

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