Variable-order fractional mean square displacement function with evolution of diffusibility

It is a challenging issue to characterize the evolution of diffusibility, which causes some complex diffusion. For the clear physical significance in some parameters of the existing fractional diffusion models, we present a modified fractional diffusion model and then establish the fractional mean square displacement (MSD) functions using a variable-order integration with memory of the order. The comparative analysis and numerical simulation demonstrate that the variable-order MSD function can characterize the evolution of the diffusibility without losing the advantage of fewer parameters.