Nonfickian effect in time and space for diffusion processes

Diffusion processes are usually simulated using the classical diffusion equation. In certain scenarios, such equation induces anomalous behavior and consequently several improvements were introduced in the literature to overcome them. One of the most popular was the replacement of the diffusion equation by an integro-differential equation. Such equation can be established considering a modification of Fick's mass flux where a delay in time is introduced. In this article, we consider mathematical models for diffusion processes that take into account a memory effect in time and space. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1589–1602, 2015