Some theoretical results on fractional-order continuous information measures

Slimane Benmahmoud

doi:10.2478/aupcsm-2024-0001

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Some theoretical results on fractional-order continuous information measures

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

Volume 23 (2024): Issue 1 (January 2024)

By: Slimane Benmahmoud

Open Access

|Feb 2024

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.

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Articles in this issue

DOI: https://doi.org/10.2478/aupcsm-2024-0001 | Journal eISSN: 2300-133X | Journal ISSN: 2081-545X

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Language: English

Page range: 5 - 12

Submitted on: Dec 27, 2022

Accepted on: Dec 12, 2023

Published on: Feb 3, 2024

Published by: Pedagogical University of Cracow

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

fractional differential entropy,

fractional joint/conditional differential entropy,

fractional relative entropy,

fractional mutual information,

Riemann-Liouville fractional integral/derivative

Related subjects:

Mathematics,

General mathematics

© 2024 Slimane Benmahmoud, published by Pedagogical University of Cracow
This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 License.

Volume 23 (2024): Issue 1 (January 2024)