MULTICONTINUUM HOMOGENIZATION FOR TIME-FRACTIONAL DIFFUSION EQUATION

Abstract

In this paper, we derive a multicontinuum time-fractional diffusion equations based on Caputo fractional derivative using a multicontinuum homogenization approach. For this purpose, we formulate cell problems with constraints considering various effects. As a result, we obtain a decomposition of the solution into macroscopic variables (continua). Assuming the smoothness of these macroscopic variables, we derive multicontinuum equations for the general case. Then, we consider a particular case of a dualcontinuum model in an isotropic medium. We present numerical experiments for two-dimensional model problems with different fractional derivative orders, demonstrating the high efficiency of the proposed approach.