Solvability of an elliptic partial differential equation with boundary condition involving fractional derivatives

We study an elliptic equation in a regular domain with a condition on the boundary involving a generalized Riemann-Liouville derivative of fractional order. The Bitsadze-Samarskii type problem is formulated for that equation. The uniqueness is proved by the maximum principle for harmonic functions....

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Bibliographic Details
Published inComplex variables and elliptic equations Vol. 59; no. 5; pp. 680 - 692
Main Authors Berdyshev, A.S., Kadirkulov, B.J., Nieto, J.J.
Format Journal Article
LanguageEnglish
Published Colchester Routledge 01.05.2014
Taylor & Francis Ltd
Subjects
Algorithms
Bitsadze-Samarskii type problem
Boundaries
Complex variables
Derivatives
Dirichlet problem
harmonic function
Kernels
Laplace equation
Mathematical analysis
Maximum principle
operator of fractional differentiation
polar kernel
solvability
Uniqueness
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Summary:We study an elliptic equation in a regular domain with a condition on the boundary involving a generalized Riemann-Liouville derivative of fractional order. The Bitsadze-Samarskii type problem is formulated for that equation. The uniqueness is proved by the maximum principle for harmonic functions. The Poisson kernel of the Dirichlet problem for the Laplace equation is used for proving the existence of a solution for the formulated problem.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:1747-6933
1747-6941
DOI:10.1080/17476933.2013.777711