From the solutions of diffusion equation to the solutions of subdiffusive one

Abstract

Starting with the Green's functions found for normal diffusion, we construct exact time-dependent Green's functions for subdiffusive equation (with fractional time derivatives), with the boundary conditions involving a linear combination of fluxes and concentrations. The method is particularly useful to calculate the concentration profiles in a multi-part system where different kind of transport occurs in each part of it. As an example, we find the solutions of subdiffusive equation for the system composed from two parts with normal diffusion and subdiffusion, respectively.

11 pages, 2 figures

References in corpus (2)

• Thermodynamics and Fractional Fokker-Planck Equations
• Diffusion on random site percolation clusters. Theory and NMR microscopy experiments with model objects

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• Extreme statistics of anomalous subdiffusion following a fractional Fokker-Planck equation: Subdiffusion is faster than normal diffusion
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• Boundary conditions at a thin membrane for normal diffusion equation which generate subdiffusion
• First passage time for subdiffusion: The nonextensive entropy approach versus the fractional model
• First passage time for $g$--subdiffusion process of vanishing particles
• Subdiffusion--absorption process in a system consisting of two different media
• Subdiffusion with particle immobilization process described by differential equation with Riemann--Liouville type fractional time derivative
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