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Complexity of an Identification Problem of Sharp Local Density Loss in Fractional Body

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Advances in Non-Integer Order Calculus and Its Applications (RRNR 2018)

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Abstract

In this paper the complexity of identification of sharp local density loss in the framework of the space-fractional continuum mechanics (s-FCM) is presented. The linear dynamic solution in the form of eigenproblem is chosen as a main factor in the objective function - both eigenvalues and eigenmodes are considered. It is shown that the solution space is extremely complicated and densely covered with local minima. The obtained results aim in the classification of the problem hardness versus s-FCM fundamental parameters, namely fractional body order and length scale.

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Acknowledgments

This work is supported by the National Science Centre, Poland, under Grant No. 2017/27/B/ST8/00351.

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Authors and Affiliations

  1. Poznan University of Technology, Poznan, Poland

    Krzysztof Szajek & Wojciech Sumelka

Authors
  1. Krzysztof Szajek
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  2. Wojciech Sumelka
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Correspondence to Krzysztof Szajek .

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Editors and Affiliations

  1. Faculty of Computer Science, Bialystok University of Technology, Białystok, Poland

    Agnieszka B. Malinowska

  2. Faculty of Computer Science, Bialystok University of Technology, Białystok, Poland

    Dorota Mozyrska

  3. Faculty of Electrical Engineering, Bialystok University of Technology, Białystok, Poland

    Łukasz Sajewski

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Szajek, K., Sumelka, W. (2020). Complexity of an Identification Problem of Sharp Local Density Loss in Fractional Body. In: Malinowska, A., Mozyrska, D., Sajewski, Ł. (eds) Advances in Non-Integer Order Calculus and Its Applications. RRNR 2018. Lecture Notes in Electrical Engineering, vol 559. Springer, Cham. https://doi.org/10.1007/978-3-030-17344-9_21

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