Super-criticism of electrochemical double layer capacitor for diffusion phenomenon: A fractional application of ultracapacitor

Abstract

Electrochemical double layer capacitors accumulate charges electrostatically and are the unique electrical storage device that can store much more energy than conventional capacitors. This manuscript proposes the mathematical modeling of electrochemical double layer capacitor on the basis of fractional differential operators. The governing equations of electrochemical double layer capacitor have been derived by means of fractional differential operators. In order to control the ratio of output to input of electrochemical double layer capacitor, the transfer functions have been investigated by employing Laplace transform method. Each transfer function obtained via Caputo (singular based kernel), Caputo-Fabrizio (non-singular but local based kernel) and Atangana-Baleanu (non-singular and nonlocal based kernel) fractional differential operators and has been graphically illustrated subject to the embedded parameters. Our results are based on the comparative transfer functions via Caputo (singular based kernel), Caputo-Fabrizio (non-singular but local based kernel) and Atangana-Baleanu (non-singular and nonlocal based kernel) differential operators suggest that the energy storage capacities of electrochemical double layer capacitor have higher magnitude, long cyclic stability, high power density and high safety in comparison with conventional dielectric capacitor.

Keywords

• Electrochemical double layer capacitor
• Transfer functions
• Laplace transform
• Caputo
• Caputo-Fabrizio
• Atangana-Baleanu