Finite domain anomalous spreading consistent with first and second laws Academic Article uri icon

abstract

  • After reviewing the problematic behavior of some previously suggested finite-interval spatial operators of the symmetric Riesz type, we create a wish list leading toward a new spatial operator suitable to use in the space-time fractional differential equation of anomalous diffusion when the transport of material is strictly restricted to a bounded domain. Based on recent studies of wall effects, we introduce a new definition of the spatial operator and illustrate its favorable characteristics. We provide two numerical methods to solve the modified space-time fractional differential equation and show particular results illustrating compliance to our established list of requirements, most important to the conservation principle and the second law of thermodynamics. ¬© 2009 Elsevier B.V. All rights reserved.

author list (cited authors)

  • Valk√≥, P. P., & Zhang, X. H.

citation count

  • 2

publication date

  • November 2010