2003/11/25 by Mark Naber, Naber, Mark
Mathematics · Physics and Astronomy · #26Axx #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #FOS: Physical sciences #Fractional Differential Equations Solutions #Mathematical Physics (math-ph) #Nonlinear Differential Equations Analysis #math-ph #math.AP #math.MP #msc:26Axx
paper · pdf · doi:10.48550/arxiv.math-ph/0311047
Accepted for publication at the journal "Fractals."
arxiv created 2003/11/25 · openalex publication_date 2003/11/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A distributed order fractional diffusion equation is considered. Distributed order derivatives are fractional derivatives that have been integrated over the order of the derivative within a given range. In this paper sub-diffusive cases are considered. That is, the order of the time derivative ranges from zero to one. The equation is solved for Dirichlet, Neumann, and Cauchy boundary conditions. The time dependence for each of the three cases is found to be a functional of the diffusion parameter. This functional is shown to have decay properties. Upper and lower bounds are computed for the functional. Examples are also worked out for comparative decay rates.