Fractional integral and differential equations for a class of Levy-type probability densities

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.