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Inverse Stable Subordinators

Published online by Cambridge University Press:  24 April 2013

M. M. Meerschaert  and
P. Straka
M. M. Meerschaert
Affiliation:
Department of Statistics and Probability, Michigan State University, East Lansing, MI 48824
P. Straka*
Affiliation:
School of Mathematics, University of Manchester, Manchester, M13 9PL, United Kingdom
*
⋆ Corresponding author. E-mail: mcubed@unr.edu
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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.

Keywords

fractional derivativesubordinatorgoverning equationhitting time
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 8 , Issue 2: Anomalous diffusion , 2013 , pp. 1 - 16
Copyright
© EDP Sciences, 2013

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