On the behavior of distributed networks of fractional-order capacitors
Year: 2025
Type: article
Abstract: Fractional calculus has seen tremendous applications in the past couple of decades particularly in the electrochemistry field for the modeling of anomalous dynamics at electrode/electrolyte interfaces. At the core of this is the fractional-order capacitor (also known as the constant phase element (CPE)), which is a non-ideal capacitive model whose impedance is z c ( s ) = 1 / ( C α s α ) ( s = j ω , C α > 0 , 0 < α < 1 ), and its current–voltage relationship is given by the Caputo fractional-order derivative i c ( t ) = C α 0 D t α v c ( t ) . The CPE has been successfully used for the modeling of impedance spectroscopy data and time-domain response of a wide range of electrochemical systems. However, a CPE of single-valued parameters can be limited in terms of modeling capability, thus a more general approach of distributed network of CPEs with multi-valued pseudocapacitances and orders is becoming necessary to investigate. In this study, we examine the behavior of such networks of CPEs, each of which is described by the Caputo fractional current–voltage equation, but with a non-negative, time-invariant weight function ϕ ( α ) for the order α . The frequency-domain behavior as well as the time-domain response to a step current excitation are derived for two special cases of ϕ ( α ) including the case of ϕ ( α ) = ∑ i C α i δ ( α − α i ) corresponding to a (discrete) network of parallel-connected CPEs of different fractional orders α i , and different pseudocapacitances
Institutions: University of Sharjah, University of Patras
Language: English
Subfield: Modeling and Simulation
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,325
OpenAlex ID: W4415164638