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Determination of the fractional order in semilinear subdiffusion equations

  • Mykola Krasnoschok , Sergei Pereverzyev , Sergii V. Siryk and Nataliya Vasylyeva EMAIL logo
Published/Copyright: July 11, 2020

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.

Acknowledgements

This work is partially supported by Grant H2020-MSCA-RISE-2014 Project number 645672 (AMMODIT: Approximation Methods for Molecular Modelling and Diagnosis Tools). The paper has been finalized during the visit of the first, third and fourth authors to Johann Radon Institute (RICAM), Linz. The hospitality and perfect working conditions of RICAM are gratefully acknowledged.

The authors are grateful to the anonymous referees for useful suggestions and comments.

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Received: 2019-04-20
Published Online: 2020-07-11
Published in Print: 2020-06-25

© 2020 Diogenes Co., Sofia

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