<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>By rewriting the differential entropy in a form of a differ-integral function’s limit, and deforming the ordinary derivative to a fractional-order one, we derive in this paper a novel generalized fractional-order differential entropy along with its related information measures. When the order of fractional differentiation <italic>α</italic> → 1, the ordinary Shannon’s differential entropy is recovered, which corresponds to the results from first-order ordinary differentiation.</p>
</abstract>

By rewriting the differential entropy in a form of a differ-integral function’s limit, and deforming the ordinary derivative to a fractional-order one, we derive in this paper a novel generalized fractional-order differential entropy along with its related information measures. When the order of fractional differentiation α → 1, the ordinary Shannon’s differential entropy is recovered, which corresponds to the results from first-order ordinary differentiation.

Some theoretical results on fractional-order continuous information measures

Department of Electronic Engineering University of M’sila

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.

{"article-title":"Some theoretical results on fractional-order continuous information measures"}

By rewriting the differential entropy in a form of a differ-integral function’s limit, and deforming the ordinary derivative to a fractional-order one, we...

Some theoretical results on fractional-order continuous information measures

Published Online: Feb 03, 2024

Page range: 5 - 12

Received: Dec 27, 2022

Accepted: Dec 12, 2023

DOI: https://doi.org/10.2478/aupcsm-2024-0001

Keywords
fractional differential entropy, fractional joint/conditional differential entropy, fractional relative entropy, fractional mutual information, Riemann-Liouville fractional integral/derivative

© 2024 Slimane Benmahmoud, published by Sciendo

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.

Some theoretical results on fractional-order continuous information measures

Published Online: Feb 03, 2024

Page range: 5 - 12

Received: Dec 27, 2022

Accepted: Dec 12, 2023

DOI: https://doi.org/10.2478/aupcsm-2024-0001

Keywordsfractional differential entropy, fractional joint/conditional differential entropy, fractional relative entropy, fractional mutual information, Riemann-Liouville fractional integral/derivative

© 2024 Slimane Benmahmoud, published by Sciendo

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.

Keywords
fractional differential entropy, fractional joint/conditional differential entropy, fractional relative entropy, fractional mutual information, Riemann-Liouville fractional integral/derivative