Response to "Comment on 'Origin of the Curie--von Schweidler law and the fractional capacitor from time-varying capacitance [J. Pow. Sources 532 (2022) 231309]' "

TL;DR

This paper defends a recent theory of capacitors based on fractional calculus, clarifying physical foundations and addressing critiques to strengthen its relevance for materials science and engineering applications.

Contribution

It provides a rebuttal to critiques of their capacitor model, reinforcing the physical basis and significance of their fractional calculus approach.

Findings

Clarifies physical underpinnings of fractional capacitor models

Addresses and refutes critiques based on fractional calculus standards

Strengthens the theoretical foundation for materials science applications

Abstract

We welcome Allagui et al.'s discussions about our recent paper that has proposed revisions to the existing theory of capacitors. It gives us an opportunity to emphasize on the physical underpinnings of the mathematical expressions that are relevant for modeling using fractional derivatives. The concerns raised by Allagui et al. are found to be quite questionable when examined in light of the established standard results of fractional calculus. Consequently, the inferences that they have drawn are not true. Finally, we would like to thank Allagui et al. because this subsequent Response to their Comment has actually led to a further consolidation of our results that are supposed to be significant for materials science as well as for fractional control systems and engineering.