Variable-Order Fractional Mean Square Displacement Function with Evolution of Diffusibility

摘要

Recently, several variable-order fractional diu000busion models were proposed, however it is still unclear which variable-order fractional calculus (VFC) definition is appropriate for the diu000busion model among many VFC definitions. In this letter, two VFC definitions are selected to establish the mean square displacement (MSD) function of the variable-order fractional diu000busion model. From the analysis and numerical simulation of MSD behaviors, the appropriate VFC definition is obtained. In addition, it has been known that the order function can reflect the evolution of diu000busibility.