Variable-order fractional differential operators in anomalous diffusion modeling

The purpose of this paper is to offer a unified discussion of variable-order differential operators in anomalous diffusion modeling. The characteristics of the new models, in contrast to constant-order fractional diffusion models, change with time, space, concentration or other independent quantities. We introduced a classification of variable-order fractional diffusion models based on the possible physical origins which prompt the variable-order. Some potential applications of the variable-order fractional diffusion models are also discussed.