title: FRACTIONAL PEARSON DIFFUSIONS.
abstract: Pearson diffusions are governed by diffusion equations with polynomial coefficients. Fractional Pearson diffusions are governed by the corresponding time-fractional diffusion equation. They are useful for modeling sub-diffusive phenomena, caused by particle sticking and trapping. This paper provides explicit strong solutions for fractional Pearson diffusions, using spectral methods. It also presents stochastic solutions, using a non-Markovian inverse stable time change.
authors.affiliation: Cardiff School of Mathematics, Cardiff University, Senghennydd Road, Cardiff CF24 4YH, UK, LeonenkoN@cardiff.ac.uk , URL : http://www.cardiff.ac.uk/maths/contactsandpeople/profiles/leonenkoN.html.
authors.forename: Nikolai N
authors.initials: NN
authors.lastname: Leonenko
authors.forename: Mark M
authors.initials: MM
authors.lastname: Meerschaert
authors.forename: Alla
authors.initials: A
authors.lastname: Sikorskii
keywords: Mittag-Leffler function; Pearson diffusion; eigenfunction expansion; fractional derivative; hitting time; stable process