title: TRANSIENT ANOMALOUS SUB-DIFFUSION ON BOUNDED DOMAINS.
abstract: This paper develops strong solutions and stochastic solutions for the tempered fractional diffusion equation on bounded domains. First the eigenvalue problem for tempered fractional derivatives is solved. Then a separation of variables and eigenfunction expansions in time and space are used to write strong solutions. Finally, stochastic solutions are written in terms of an inverse subordinator.
authors.affiliation: Department of Statistics and Probability, Michigan State University, East Lansing, MI 48823. mcubed@stt.msu.edu URL: http://www.stt.msu.edu/~mcubed/
authors.forename: Mark M
authors.initials: MM
authors.lastname: Meerschaert
authors.affiliation: Department of Mathematics and Statistics, 221 Parker Hall, Auburn University, Auburn, AL 36849. nane@auburn.edu URL: http://www.auburn.edu/~ezn0001/
authors.forename: Erkan
authors.initials: E
authors.lastname: Nane
authors.affiliation: Department of Mathematics, Indian Institute of Technology Bombay, Powai, Mumbai 400076 India. pv@math.iit.ac.in.
authors.forename: P
authors.initials: P
authors.lastname: Vellaisamy
keywords: Cauchy problem; Fractional diffusion; boundary value problem; tempered stable