Exact solution for the electrical response of a constant phase element with a series resistance to linear voltage sweep

A resistance in series with a constant phase element (CPE) of frequency-dependent impedance given by the power law function is commonly used for the analysis of steady-state frequency response data exhibiting non-purely capacitive behavior. This is the case in most (bio)(electro)chemical systems including dielectrics, batteries, supercapacitors, capacitive deionization units, biological tissues and bioelectrodes. Passing to the time domain, the current, voltage and charge of the system are governed by differential equations with non-integer, fractional-order operators. The purpose of this study is to provide the exact analytical expressions for the electrical response of an -CPE model under linear sweep voltammetry with the use of the Laplace transform method. The electrical variables are expressed in terms of special functions regularly encountered with fractional calculus such as the Fox’s -function and the Mittag-Leffler function, and can be used for modeling non-ideal devices as well as extracting their characteristic parameters.