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Non-exponential discharge dynamics in electrochemical capacitors

We study the non-exponential, power-law charge/voltage-time behavior of a supercapacitor when it is discharged into a constant resistive load. The standard evolution equation dn(t)=dt = -λn(t) where λ is an inverse time constant and n(t) can represent here charge or voltage is modifed instead to be dn(t)=dt = -λ[n(t)]q relating the rate of change of n(t) to a power law function of n(t). This leads to the q-exponential function which shows much better fitting capability to the experimental results obtained on a commercial capacitive device when compared with the traditional exponential decay.