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Alla Sikorskii, Michigan State University (NOTE TIME AND ROOM!!): Fractional differential equations are an important and useful tool in many areas of science and engineering. In a heterogeneous environment, the coefficients of the diffusion equation will naturally vary in space. Pearson diffusions form a tractable class of variable coefficient diffusion models with polynomial coefficients. Fractional Pearson diffusions are governed by the corresponding time-fractional diffusion equation.

We provide explicit strong solutions for fractional Pearson diffusion equations, using spectral methods and stochastic solutions, using a non-Markovian time change. We also present the correlation structure of fractional Pearson diffusions in steady state.