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An entropy paradox free fractional diffusion equation
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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.
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Diffusion equation Entropy production paradox Rényi entropy Shannon entropy Stable distribution Tsallis entropy Unified fractional derivative Analysis Statistical and Nonlinear Physics Statistics and Probability