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math.AP2019
On viscosity solutions of space-fractional diffusion equations of Caputo type
Tokinaga Namba, Piotr Rybka
We study a fractional diffusion problem in the divergence form in one space dimension. We define a notion of the viscosity solution. We prove existence of viscosity solutions to th…
math.AP2019
Some comments on using fractional derivative operators in modeling non-local diffusion processes
Tokinaga Namba, Piotr Rybka, Vaughan Voller
We start with a general governing equation for diffusion transport, written in a conserved form, in which the phenomenological flux laws can be constructed in a number of alternati…