Abstract
In this paper, we investigate solvability of fractional analogs of the Dirichlet and Neumann boundary-value problems for the Laplace equation. Operators of fractional differentiation in the Riemann–Liouville and Caputo sense are considered as boundary operators. The considered problems are solved by reducing them to Fredholm integral equations. Theorems on existence and uniqueness of solutions of the problems are proved.
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Acknowledgements
The work was supported by a grant from the Ministry of Science and Education of the Republic of Kazakhstan (Grant no. AP05131268).
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Turmetov, B., Nazarova, K. On Fractional Analogs of Dirichlet and Neumann Problems for the Laplace Equation. Mediterr. J. Math. 16, 59 (2019). https://doi.org/10.1007/s00009-019-1347-5
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DOI: https://doi.org/10.1007/s00009-019-1347-5