Abstract
AbstractIn this research, many novel expressions for time domain responses of fractance device to various often cited inputs have been proposed. Unlike the previous ones, our expressions have been derived based on the Caputo fractional derivative by also concerning the dimensional consistency with the integer order device based responses and the different between two types of fractance device i.e. fractional order inductor and fractional order capacitor. These previous expressions have been derived based on the Riemann-Liouvielle fractional derivative which has certain features that leads to contradictions and additional modeling difficulties unlike the Caputo fractional derivative. Our new expressions are applicable to both fractional order inductor and capacitor with arbitrary order. They are also applicable to any subject which its electrical characteristic can be modeled based on the fractance device. With our expressions and numerical simulations, the time domain behavioral analysis of both fractance...
Highlights
Fractance device is an electronic device with fractional order impedance function i.e. such order can be any real value between −1 and 1
The novel expressions of time domain responses of fractance device excited by various renowned inputs e.g. impulse, step, ramp, parabolic, trigonometric and arbitrary periodic input etc., have been derived in this research by considering the formerly ignored dimensional consistency and different between both types of fractance device i.e. the fractional order inductor and capacitor
The derived expressions are applicable to the fractance device of both types with arbitrary order. They are applicable to any subject that its electrical characteristic can be modeled by using the fractance device such as those mentioned above where the applications to the supercapacitors, lossy magnetic core inductive coils and Lithium-ion battery have been demonstrated
Summary
Fractance device is an electronic device with fractional order impedance function i.e. such order can be any real value between −1 and 1. The fractance device which the phase of its voltage always leads that of its current has positive order, and vice versa are referred to as the fractional order inductor and fractional order capacitor respectively This device is often cited in various scientific disciplines e.g. biomedical engineering (Barsoukov & Macdonald, 2005; Inaba, Manabe, Tsuji, & Iwamoto, 1995; Jesus, MacHado, & Cunha, 2008; Tang et al, 2009), control system (Charef, 2006; Jifeng & Yuankai, 2005; Vinagre & Feliu, 2007), electronic circuit and electrical engineering (Ahmad, El-khazali, & Elwakil, 2001; Dorčák, Terpák, Petráš, & Dorčáková, 2007; Freeborn, Maundy, & Elwakil, 2013; Ma, Zhou, Li, & Chen, 2016; Schäfer & Krüger, 2006; Stanislavsky, 2005) etc. The Caputo fractional derivative which has been adopted in this research, can be given as follows (Atangana & Secer, 2013; Valério et al, 2013):
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
