On Hilfer's objection to the fractional time diffusion equation

Physica A: Statistical Mechanics and its Applications

Volumn 373, Issue , 2007, Pages 231-236

  Barkai, E ^a   Sokolov, I M ^b  

^a BAR ILAN UNIVERSITY   (Israel)

^b HUMBOLDT UNIVERSITY   (Germany)

Author keywords

Continuous time random walks; Continuum limit; Fractional diffusion equation

Indexed keywords

CONTINUUM MECHANICS; CONVERGENCE OF NUMERICAL METHODS; MATHEMATICAL MODELS; PROBABILITY DENSITY FUNCTION; THEOREM PROVING;

CONTINUOUS TIME RANDOM WALK (CTRW); CONTINUUM LIMIT; FRACTIONAL DIFFUSION EQUATIONS;

DIFFUSION;

EID: 33750488103     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physa.2006.05.022     Document Type: Article

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20. 2 / 2 for k → 0, however, then the fractional framework is valid only in the long time limit. Thus, in this sense Mittag-Leffler waiting times are similar to all other longed-tailed waiting times PDFs, as we show in the manuscript. Namely Mittag-Leffler waiting time PDFs may yield a fractional behavior only in the limit of long times. Note that Mittag-Leffler functions are known as a natural generalization of the exponential function in the context of anomalous diffusion [2].
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