A non-Fickian diffusion equation

A non-Fickian diffusion equation, which differs from the usual (Fickian) diffusion equation by having an additional, second-order derivative term in time, is considered to describe the dynamics of a Brownian particle. Some useful perspectives on this generalized diffusion equation are presented, particularly with respect to the effect of a potential field. Two quantities of physical interest, namely the mean square displacement and the particle flux at an absorbing boundary, are considered in the process of a comparative study of the two diffusion equations. We also discuss the applicability of the non-Fickian diffusion equation to some systems of physical and practical interest.