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 fractional order. The fundamental solutions of these equation
s provide probability density functions, evolving on time or variable in space, which are related to the class of stable distributions. This property is a noteworthy generalization of what happens for the standard diffusion equation and can be relevant in treating financial and economical problems where the stable probability distributions play a key role.
