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Determination of the Fractional Order in Semilinear Subdiffusion Equations

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Abstract

We analyze the inverse boundary value-problem to determine the fractional order ν of nonautonomous semilinear subdiffusion equations with memory terms from observations of their solutions during small time. We obtain an explicit formula reconstructing the order. Based on the Tikhonov regularization scheme and the quasi-optimality criterion, we construct the computational algorithm to find the order ν from noisy discrete measurements. We present several numerical tests illustrating the algorithm in action.

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Authors and Affiliations

  1. G. Batyuka Str. 19, 84100, Sloviansk, Ukraine

    Mykola Krasnoschok

  2. Altenbergstrasse 69, 4040, Linz, Austria

    Sergei Pereverzyev

  3. National Technical University of Ukraine, “Igor Sikorsky Kyiv Polytechnic Institute”, Prospect Peremohy 37, 03056, Kyiv, Ukraine

    Sergii V. Siryk

  4. Institute of Applied Mathematics & Mechanics of NAS of Ukraine, G. Batyuka Str. 19, 84100, Sloviansk, Ukraine

    Nataliya Vasylyeva

Authors
  1. Mykola Krasnoschok
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  2. Sergei Pereverzyev
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  3. Sergii V. Siryk
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  4. Nataliya Vasylyeva
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Correspondence to Mykola Krasnoschok.

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Krasnoschok, M., Pereverzyev, S., Siryk, S.V. et al. Determination of the Fractional Order in Semilinear Subdiffusion Equations. Fract Calc Appl Anal 23, 694–722 (2020). https://doi.org/10.1515/fca-2020-0035

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  • DOI: https://doi.org/10.1515/fca-2020-0035

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