Fractional Pearson diffusions

Leonenko, Nikolai N. ORCID: https://orcid.org/0000-0003-1932-4091, Meerschaert, M. M. and Sikorskii, A. 2013. Fractional Pearson diffusions. Journal of Mathematical Analysis and Applications 403 (2) , pp. 532-546. 10.1016/j.jmaa.2013.02.046

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Abstract

Pearson diffusions are governed by diffusion equations with polynomial coefficients. Fractional Pearson diffusions are governed by the corresponding timefractional 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.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Schools > Mathematics
Subjects:	Q Science > QA Mathematics
Uncontrolled Keywords:	Pearson diffusion; Fractional derivative; Eigenfunction expansion; Stable process; Hitting time; Mittag-Leffler function
Publisher:	Elsevier
ISSN:	0022-247X
Last Modified:	24 Oct 2022 10:38
URI:	https://orca.cardiff.ac.uk/id/eprint/45212

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