分野別セミナー

Abstract: Anomalous diffusion has been the subject of extensive research in recent years, with numerous publications addressing different aspects of this phenomenon. The growing number of applications that can be described by anomalous diffusivity has led to increased interest in this area of study. While previous research has explored the dependence of diffusion coefficients on space, there have been no published results on the dependence of these coefficients on both space and time variables until now. Three years ago, we provided exact solutions for anomalous diffusion equations with a diffusion coefficient function that depended only on the space variable. In this study, we extend our previous work to include the time variable in the diffusion coefficient function. We derive closed-form solutions for time-fractional anomalous diffusion equations with diffusivity coefficients that depend on both space and time variables. These solutions are expressed in Fox-H and generalized Wright functions, which are commonly used in anomalous diffusion equations. This development allows for the modeling of processes that were previously inaccessible.