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Fractional diffusion in inhomogeneous media. (English) Zbl 1082.76097
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:
76R50Diffusion (fluid mechanics)
76M35Stochastic analysis (fluid mechanics)