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Application of SubIval, a Method for Fractional-Order Derivative Computations in IVPs

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Theory and Applications of Non-integer Order Systems

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 407))

Abstract

The paper concerns a numerical method for the computations of the fractional derivative in initial value problems. The method bases on a partition of the integrodifferentiation interval into subintervals. It has been referred to previously as the subinterval-based method and is now called SubIval (for simpler reference). The subintervals are modified during a time stepping process – this is determined by an original subinterval dynamics algorithm. The method is mainly built in order to aid in solving problems of circuit theory. Hence, two examples have been introduced to ascertain the method, where both use a fractional order capacitor and a fractional order coil.

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Authors and Affiliations

  1. Institute of Electric Engineering and Computer Science, Silesian University of Technology, Akademicka 10, 44-100, Gliwice, Poland

    Marcin Sowa

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  1. Marcin Sowa
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Correspondence to Marcin Sowa .

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Editors and Affiliations

  1. Institute of Automatic Control, Silesian University of Technology Institute of Automatic Control, Gliwice, Poland

    Artur Babiarz

  2. Institute of Automatic Control, Silesian University of Technology Institute of Automatic Control, Gliwice, Poland

    Adam Czornik

  3. Institute of Automatic Control, Silesian University of Technology Institute of Automatic Control, Gliwice, Poland

    Jerzy Klamka

  4. Institute of Automatic Control, Silesian University of Technology Institute of Automatic Control, Gliwice, Poland

    Michał Niezabitowski

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Sowa, M. (2017). Application of SubIval, a Method for Fractional-Order Derivative Computations in IVPs. In: Babiarz, A., Czornik, A., Klamka, J., Niezabitowski, M. (eds) Theory and Applications of Non-integer Order Systems. Lecture Notes in Electrical Engineering, vol 407. Springer, Cham. https://doi.org/10.1007/978-3-319-45474-0_43

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  • DOI: https://doi.org/10.1007/978-3-319-45474-0_43

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-45473-3

  • Online ISBN: 978-3-319-45474-0

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