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On Fractional Analogs of Dirichlet and Neumann Problems for the Laplace Equation

  • Batirkhan TurmetovEmail author
  • Kulzina Nazarova
Article
  • 7 Downloads

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.

Keywords

Laplace equation Dirichlet problem Neumann problem Fractional derivative Riemann–Liouville operator Caputo operator uniqueness existence 

Mathematics Subject Classification

Primary 31A05 Secondary 35J05 

Notes

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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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Ahmet Yesevi UniversityTurkistanKazakhstan

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