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

Abro, Kashif Ali and Hameed Shaikh, Pervaiz and Go´mez-Aguilar, J.F. (2019) Analysis of De-Levie’s model via modern fractional differentiations: An application to supercapacitor. Analysis of De-Levie’s model via modern fractional differentiations: An application to supercapacitor, 61 (12). pp. 1375-1384. ISSN 1110-0168

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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 trans�forms 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 deriva�tive based on singular, non- singular and non-local kernels. Finally, our results suggest that construc�tion of the electrodes with optimal utilization can be controlled by fractional approaches.

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