Space‐time fractional Dirichlet problems
Abstract
This paper establishes explicit solutions for fractional diffusion problems on bounded domains. It also gives stochastic solutions, in terms of Markov processes time‐changed by an inverse stable subordinator whose index equals the order of the fractional time derivative. Some applications are given, to demonstrate how to specify a well‐posed Dirichlet problem for space‐time fractional diffusions in one or several variables. This solves an open problem in numerical analysis.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Aug 07, 2018
- Source ID
- 10.1002/mana.201700111
Entities
People
- Boris Baeumer
- Mark M. Meerschaert
- Tomasz Luks
Organizations
- Army Research Office
- Michigan State University
- National Science Foundation
- Royal Society Te Apārangi
- University of Otago
- University of Paderborn