  The stochastic solution to diffusion equations with polynomial coefficients
is called a Pearson diffusion. If the time derivative is replaced by a
distributed fractional derivative, the stochastic solution is called a
fractional Pearson diffusion. This paper develops a formula for the covariance
function of a fractional Pearson diffusion in steady state, in terms of
generalized Mittag-Leffler functions. That formula shows that fractional
Pearson diffusions are long-range dependent, with a correlation that falls off
like a power law, whose exponent equals the smallest order of the distributed
fractional derivative.
