Abstract
The paper presents an analysis of the fractional electrical circuit in the transient state described by the fractional-order state-space equations. General solutions to the fractional state-space equations containing two types of definitions of fractional derivative: Caputo fractional order derivative and the Conformable Fractional Derivative (CFD) definitions. The solutions are given in three cases: (1) nonzero initial conditions and zero input signal, (2) the input signal in the form of a step function and zero initial conditions; (3) the general case where the input and initial conditions are nonzero. The results for voltages across the capacitors for derivatives of fractional orders equal \(\alpha =0.7; 0.8; 0.9\) are shown. The comparison of those two definitions is presented and discussed.
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Acknowledgements
The paper supported by research project MB/WE/3/2017 (the first author) and by National Science Centre in Poland under the work no. 2014/13/B/ST7/03467 (the second author).
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Piotrowska, E., Rogowski, K. (2019). Analysis of Fractional Electrical Circuit Using Caputo and Conformable Derivative Definitions. In: Ostalczyk, P., Sankowski, D., Nowakowski, J. (eds) Non-Integer Order Calculus and its Applications. RRNR 2017. Lecture Notes in Electrical Engineering, vol 496. Springer, Cham. https://doi.org/10.1007/978-3-319-78458-8_16
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DOI: https://doi.org/10.1007/978-3-319-78458-8_16
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