Generalized theory of diffusive stresses associated with the time-fractional diffusion equation and nonlocal constitutive equations for the stress tensor

The theory of diffusive stresses based on the time-fractional diffusion equation with the Liouville-Caputo derivative is discussed. The diffusion process is characterized by the chemical potential tensor and the concentration tensor. Eliminating the chemical potential tensor and the concentration tensor from the constitutive equations for the stress tensor, the space-time-nonlocal equations for the mean stress and the deviatoric stress are obtained with the kernel being the Wright function. (C) 2016 Elsevier Ltd. All rights reserved.