Distributed-order fractional diffusions on bounded domains

By Mark M. Meerschaert, Erkan Nane, Palaniappan Vellaisamy. 2009

142 citations recorded by the source corpus.

Fractional derivatives can be used to model time delays in a diffusion process. When the order of the fractional derivative is distributed over the unit interval, it is useful for modeling a mixture of delay sources. This paper provides explicit strong solutions and stochastic analogues for distributed-order time-fractional diffusion equations on bounded domains, with Dirichlet boundary conditions.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/35e42559f30f7b8dc09eabd6978774e8549a513b

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In Applied Mathematics

In Modeling and Simulation

In Numerical Analysis

Citations in the corpus

Analytical solutions for the multi-term time–space Caputo–Riesz fractional advection–diffusion equations on a finite domain (2012, background): “[22] derived explicit strong solutions and stochastic analogues for distributed-order time-fractional diffusion equations on bounded domains, with Dirichlet boundary conditions.”
Space-time fractional diffusion on bounded domains (2011, background): “The paper [22] solves distributed-order time-fractional diffusion equations ∂ t u = ∆u on bounded domains.”
Asymptotic properties of Brownian motion delayed by inverse subordinators (2013, unknown): “Another interesting example is the distributed order fractional diffusion equations [12, 24, 38], which correspond to the case f(u) = ∫∞ 0 (1 − e−ux) ν(dx) with ν(t,∞) = ∫ 1 0 t−β μ(dβ).”