Fractional diffusion in inhomogeneous media. (English) Zbl 1082.76097

Chechkin, A. V.; Gorenflo, R.; Sokolov, I. M.

J. Phys. A, Math. Gen. 38, No. 42, L679-L684 (2005).

Summary: Starting from the continuous time random walk scheme with the space-dependent waiting-time probability density function, we obtain the time-fractional diffusion equation with varying in space fractional order of time derivative. As an example, we study the evolution of a composite system consisting of two separate regions with different subdiffusion exponents and demonstrate the effects of non-trivial drift and subdiffusion whose laws are changed in the course of time.

MSC:

76R50	Diffusion
76M35	Stochastic analysis applied to problems in fluid mechanics

Keywords:

time random walk scheme; subdiffusion