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Axioms 2016, 5(1), 6; doi:10.3390/axioms5010006

Entropy Production Rate of a One-Dimensional Alpha-Fractional Diffusion Process

Department of Mathematics, Physics, and Chemistry, Beuth Technical University of Applied Sciences, Luxemburger Str. 10, 13353 Berlin, Germany
Academic Editor: Hans J. Haubold
Received: 30 December 2015 / Accepted: 2 February 2016 / Published: 5 February 2016
View Full-Text   |   Download PDF [237 KB, uploaded 5 February 2016]

Abstract

In this paper, the one-dimensional α-fractional diffusion equation is revisited. This equation is a particular case of the time- and space-fractional diffusion equation with the quotient of the orders of the time- and space-fractional derivatives equal to one-half. First, some integral representations of its fundamental solution including the Mellin-Barnes integral representation are derived. Then a series representation and asymptotics of the fundamental solution are discussed. The fundamental solution is interpreted as a probability density function and its entropy in the Shannon sense is calculated. The entropy production rate of the stochastic process governed by the α-fractional diffusion equation is shown to be equal to one of the conventional diffusion equation. View Full-Text
Keywords: Caputo fractional derivative; Riesz fractional derivative; α-fractional diffusion equation; Mellin transform; fundamental solution; Mellin-Barnes integrals; entropy; entropy production rate Caputo fractional derivative; Riesz fractional derivative; α-fractional diffusion equation; Mellin transform; fundamental solution; Mellin-Barnes integrals; entropy; entropy production rate
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Luchko, Y. Entropy Production Rate of a One-Dimensional Alpha-Fractional Diffusion Process. Axioms 2016, 5, 6.

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