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On an inverse problem of the Bitsadze–Samarskii type for a parabolic equation of fractional order

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Abstract

In this paper, for a fractional order equation with a fractional differentiation operator in the sense of Gerasimov–Caputo, we study a nonlocal problem of the Bitsadze–Samarskii type. To prove uniqueness and existence theorems for a regular solution to this problem, the spectral method is used. Spectral questions for the corresponding ordinary differential equation are investigated, eigenfunctions and associated functions are found, and their basis property is proved. For such equations, we study the adjoint problem too.

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Author notes

  1. Baxtiyar Kadirkulov and Muhammadali Jalilov contributed equally to this work.

Authors and Affiliations

  1. Department of Differential Equations and Their Applications, Institute of Mathematics, Uzbekistan Academy of Science, Student Town Str., 100174, Tashkent, Uzbekistan

    Ravshan Ashurov

  2. School of Engineering, Central Asian University, 264, Milliy Bog Str., 111221, Tashkent, Uzbekistan

    Ravshan Ashurov

  3. Department of Mathematics and Information Technologies, Tashkent State University of Oriental Studies, Amir Temur Str., 100060, Tashkent, Uzbekistan

    Baxtiyar Kadirkulov

  4. Fergana State University, Murabbiylar Str., 150100, Fergana, Uzbekistan

    Muhammadali Jalilov

Authors
  1. Ravshan Ashurov
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  2. Baxtiyar Kadirkulov
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  3. Muhammadali Jalilov
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All the authors equally contributed in this work.

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Correspondence to Ravshan Ashurov.

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Ashurov, R., Kadirkulov, B. & Jalilov, M. On an inverse problem of the Bitsadze–Samarskii type for a parabolic equation of fractional order. Bol. Soc. Mat. Mex. 29, 70 (2023). https://doi.org/10.1007/s40590-023-00542-y

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