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1 October 2018 Analysis the conformable fractional derivative and Caputo definitions in the action of an electric circuit containing a supercapacitor
Ewa Piotrowska
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Proceedings Volume 10808, Photonics Applications in Astronomy, Communications, Industry, and High-Energy Physics Experiments 2018; 108081T (2018) https://doi.org/10.1117/12.2501384
Event: Photonics Applications in Astronomy, Communications, Industry, and High-Energy Physics Experiments 2018, 2018, Wilga, Poland
Abstract
The paper presents an analysis of the electrical circuit with the supercapacitor in the transient state described by the fractional-order state-space equations. General solutions to the fractional state-space equations developed for two types of definitions of fractional derivative: Caputo and the Conformable Fractional Derivative (CDF). The voltage characteristics of the charge supercapacitor were compared with the results of analytical tests. The voltage was measured on the supercapacitor. Next was determined with of solution are the best fit compared: classic case solution and solution using the fractional order definition. The tests were carried out for three different resistance values. Using the method of least-squares optimization the analytical results and measurements were compared with each other by the function of matching error.
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Ewa Piotrowska "Analysis the conformable fractional derivative and Caputo definitions in the action of an electric circuit containing a supercapacitor", Proc. SPIE 10808, Photonics Applications in Astronomy, Communications, Industry, and High-Energy Physics Experiments 2018, 108081T (1 October 2018); https://doi.org/10.1117/12.2501384
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KEYWORDS
Resistance
Resistors
Capacitors
Calculus
Error analysis
Capacitance
Mathematical modeling
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