An Entropy Paradox Free Fractional Diffusion Equation

Author:

Ortigueira Manuel DuarteORCID

Abstract

A new look at the fractional diffusion equation was done. Using the unified fractional derivative, a new formulation was proposed, and the equation was solved for three different order cases: neutral, dominant time, and dominant space. The solutions were expressed by generalizations of classic formulae used for the stable distributions. The entropy paradox problem was studied and clarified through the Rényi entropy: in the extreme wave regime the entropy is −∞. In passing, Tsallis and Rényi entropies for stable distributions are introduced and exemplified.

Funder

Fundação para a Ciência e Tecnologia

Publisher

MDPI AG

Subject

Statistics and Probability,Statistical and Nonlinear Physics,Analysis

Reference48 articles.

1. Diffusion Equation and Stochastic Processes

2. The Mathematics of Diffusion;Crank,1979

3. Linear Fractional Diffusion-Wave Equation for Scientists and Engineers;Povstenko,2015

4. Fractional calculus - A different approach to the analysis of viscoelastically damped structures

5. Anomalous diffusion in one dimension

Cited by 2 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3