title: Stochastic solution of space-time fractional diffusion equations.
abstract: Classical and anomalous diffusion equations employ integer derivatives, fractional derivatives, and other pseudodifferential operators in space. In this paper we show that replacing the integer time derivative by a fractional derivative subordinates the original stochastic solution to an inverse stable subordinator process whose probability distributions are Mittag-Leffler type. This leads to explicit solutions for space-time fractional diffusion equations with multiscaling space-fractional derivatives, and additional insight into the meaning of these equations.
authors: Department of Mathematics, University of Nevada, Reno, Nevada 89557-0084, USA. mcubed@unr.edu
authors: Mark M
authors: MM
authors: Meerschaert
authors: David A
authors: DA
authors: Benson
authors: Hans-Peter
authors: HP
authors: Scheffler
authors: Boris
authors: B
authors: Baeumer