Affiliation:
1. Faculty of Technology , Department of Electronic Engineering University of M’sila , M’sila Algeria
Abstract
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.
Reference12 articles.
1. Boltzmann, Ludwig. “Lectures on the Principles of Mechanics.” In Theoretical Physics and Philosophical Problems editeg by B. McGuinness. Dordrecht: Springer, 1974. Cited on 5.
2. Clausius, Rudolf and Thomas Archer Hirst. The Mechanical Theory of Heat: With its Applications to the Steam-Engine and to the Physical Properties of Bodies. London: J. Van Voorst, 1867. Cited on 5.
3. Cover, Thomas M., and Joy A. Thomas. Elements of Information Theory. New-York: John Wiley & Sons, INC., 1991. Cited on 7.
4. Hilfer, Rudolf. Applications Of Fractional Calculus In Physics. Universität Mainz & Universität Stuttgart, 2000. Cited on 6.
5. Jumarie, Guy. Relative Information: Theories and Applications. Vol. 47 of Springer Series in Synergetics. Heidelberg: Springer Berlin, 2011. Cited on 6.