Vol 50, No 3 (1998)

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Fractional calculus and stable probability distributions

R. Gorenflo, F. Mainardi

Arch. Mech. 50 (3), 377-388, 1998

Keywords:


Abstract


Fractional calculus allows one to generalize the linear (one-dimensional) diffusion equation by replacing either the first time-derivative or the second space-derivative by a derivative of a fractional order. The fundamental solutions of these generalized diffusion equations are shown to provide certain probability density functions, in space or time, which are related to the relevant class of stable distributions. For the space fractional diffusion, a random-walk model is also proposed.

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