Analysis of De-Levie’s model via modern fractional differentiations: An application to supercapacitor

Abstract

De-Levie’s model has become an indispensable model for knowing a porous electrode because electrochemical supercapacitors provide electrical energy storage and they use nanoporous electrodes to store large amounts of charge. This manuscript proposes the fractional analysis of De-Levie’s model via three types of modern fractional differentiations namely Caputo, Caputo-Fabrizio and Atangana-Baleanu fractional operators. The system of ordinary coupled differential equations of De-Levie’s model have been fractionalized and coupled into equivalent form of diffusion equation. The analytic solutions of voltage are traced out by means of Fourier sine and Laplace transforms subject to the satisfaction of sinusoidal and exponential conditions. The general solutions of De-Levie’s model have been investigated in term of special and elementary functions. The graphs of comparative analysis have been depicted for voltage through three approaches of fractional derivative based on singular, non- singular and non-local kernels. Finally, our results suggest that construction of the electrodes with optimal utilization can be controlled by fractional approaches.