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Spectral representation of transition densities of fractional Pearson diffusions

Heavy-tailed fractional Pearson diffusions are a class of sub-diffusions with marginal heavy- tailed Pearson distributions: reciprocal gamma, Fisher-Snedecor and Student distributions. They are governed by the time-fractional diffusion equations with polynomial coefficients depending on the parameters of the corresponding Pearson distribution. We derive the spectral representation of transition densities of fractional Fisher-Snedecor and reciprocal - gamma diffusions, which depend heavily on the structure of the spectrum of the infinitesimal generator of the corresponding non-fractional Pearson diffusion.

Fractional diffusion, Fractional backward Kolmogorov equation, Hypergeometric function, Mittag-Leffler function, Pearson diffusion, Spectral representation, Transition density, Whittaker function

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