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An application of the fractional calculus to a class of Levy distribution functions leads to the conclusion that the Levy index (fractal dimension) mu is identical to the order of the fractional Liouville-Riemann integral operator. The corresponding fractional integral and differential equations are presented and solutions of Levy-type, one-sided probability densities are given and discussed.
T. F. Nonnenmacher (Sat,) studied this question.