Some comments on using fractional derivative operators in modeling non-local diffusion processes

We start with a general governing equation for diffusion transport, written in conserved form, which the phenomenological flux laws can be constructed number of alternative ways. pay particular attention to that account non-locality through space fractional derivative operators. The available results on well posedness equations using such are discussed. A discrete control volume numerical solution is developed and treatment boundary conditions, independent choice law, presented. properties scheme resulting from analyzed. use solutions various test problems compare operation predictive ability two based Caputo (C) Riemann–Liouville (RL) derivatives respectively. When compared C flux-law we note RL law includes an additional term, that, sense, acts as apparent advection transport. Through our show when performance flux-law, this extra term lead RL-flux predictions may physically mathematically unsound. conclude, by proposing parsimonious definition removes ambiguities associated selection between non-local derivatives.