How to Measure Subdiffusion Parameters

We propose a method to measure the subdiffusion parameter α and subdiffusion coefficient D_α which are defined by means of the relation ⟨x²⟩=2D_αΓ(1+α)t^α, where ⟨x²⟩ denotes a mean square displacement of a random walker starting from $x=0$ at the initial time $t=0$. The method exploits a membrane system where a substance of interest is transported in a solvent from one vessel to another across a thin membrane which plays here only an auxiliary role. We experimentally study a diffusion of glucose and sucrose in a gel solvent, and we precisely determine the parameters α and D_α, using a fully analytic solution of the fractional subdiffusion equation.