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On the Well-Posedness of Boundary Value Problems for a Fractional Diffusion-Wave Equation and One Approach to Solving Them

  • PARTIAL DIFFERENTIAL EQUATIONS
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Abstract

Based on earlier-established necessary nonlocal conditions that must be satisfied by all regular solutions of a fractional diffusion–wave equation in a rectangular domain, we propose a method for determining the well-posedness of nonlocal boundary value problems for this equation and a method for finding their solutions.

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Notes

  1. The ceiling of a number is the least integer that is not less than this number. In our case of \(\alpha \in (0,2)\), we have \(\lceil \alpha \rceil =1 \) if \(\alpha \in (0,1] \) and \(\lceil \alpha \rceil =2 \) if \(\alpha \in (1,2) \).

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Authors and Affiliations

  1. Institute of Applied Mathematics and Automation, Kabardino-Balkar Scientific Center, Russian Academy of Sciences, Nalchik, Kabardino-Balkarian Republic, 360000, Russia

    M. O. Mamchuev

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  1. M. O. Mamchuev
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Correspondence to M. O. Mamchuev.

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Translated by V. Potapchouck

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Mamchuev, M.O. On the Well-Posedness of Boundary Value Problems for a Fractional Diffusion-Wave Equation and One Approach to Solving Them. Diff Equat 56, 756–760 (2020). https://doi.org/10.1134/S0012266120060087

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  • DOI: https://doi.org/10.1134/S0012266120060087

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