title: INVERSE STABLE SUBORDINATORS.
abstract: The inverse stable subordinator provides a probability model for time-fractional differential equations, and leads to explicit solution formulae. This paper reviews properties of the inverse stable subordinator, and applications to a variety of problems in mathematics and physics. Several different governing equations for the inverse stable subordinator have been proposed in the literature. This paper also shows how these equations can be reconciled.
authors.affiliation: Department of Statistics and Probability, Michigan State University, East Lansing, MI 48824.
authors.forename: Mark M
authors.initials: MM
authors.lastname: Meerschaert
authors.affiliation: School of Mathematics, University of Manchester, Manchester, M13 9PL, United Kingdom.
authors.forename: Peter
authors.initials: P
authors.lastname: Straka
keywords: fractional derivative; governing equation; hitting time; subordinator