TY - JOUR
T1 - An entropy paradox free fractional diffusion equation
AU - Ortigueira, Manuel Duarte
N1 -
info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F00066%2F2020/PT#
PY - 2021/12
Y1 - 2021/12
N2 - 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.
AB - 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.
KW - Diffusion equation
KW - Entropy production paradox
KW - Rényi entropy
KW - Shannon entropy
KW - Stable distribution
KW - Tsallis entropy
KW - Unified fractional derivative
UR - http://www.scopus.com/inward/record.url?scp=85120156512&partnerID=8YFLogxK
U2 - 10.3390/fractalfract5040236
DO - 10.3390/fractalfract5040236
M3 - Article
AN - SCOPUS:85120156512
SN - 2504-3110
VL - 5
JO - Fractal and Fractional
JF - Fractal and Fractional
IS - 4
M1 - 236
ER -