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 = -lambda n(t) where lambda is an inverse time constant and n(t) can represent here charge or voltage is modified instead to be dn(t)/dt = -lambda[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.