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On Solvability of a Boundary Value Problem for a Nonlocal Biharmonic Equation with a Fractional Order Boundary Operator

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Abstract

In this paper, using an orthogonal matrix in space \(R^{n}\), the notion of a nonlocal biharmonic operator is introduced. For the corresponding nonlocal biharmonic equation, solvability of boundary value problems with fractional conformable derivatives is studied. For the considered problems, theorems on the existence and uniqueness of solutions are proved. Necessary and sufficient conditions for solvability of the studied problems are obtained and integral representations of solutions are presented.

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Authors and Affiliations

  1. Khoja Akhmet Yassawi International Kazakh-Turkish University, 161200, Turkestan, Kazakhstan

    K. I. Usmanov, B. Kh. Turmetov & K. Zh. Nazarova

Authors
  1. K. I. Usmanov
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  2. B. Kh. Turmetov
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  3. K. Zh. Nazarova
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Correspondence to K. I. Usmanov, B. Kh. Turmetov or K. Zh. Nazarova.

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(Submitted by A. T. Assanova)

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Usmanov, K.I., Turmetov, B.K. & Nazarova, K.Z. On Solvability of a Boundary Value Problem for a Nonlocal Biharmonic Equation with a Fractional Order Boundary Operator. Lobachevskii J Math 43, 3298–3309 (2022). https://doi.org/10.1134/S1995080222140359

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  • DOI: https://doi.org/10.1134/S1995080222140359

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