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On a generalization of the Neumann problem for the Laplace equation
Author(s) -
Turmetov B.,
Nazarova K.
Publication year - 2020
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201800219
Subject(s) - mathematics , laplace's equation , uniqueness , generalization , mathematical analysis , neumann boundary condition , operator (biology) , uniqueness theorem for poisson's equation , hadamard transform , laplace transform , fredholm integral equation , boundary value problem , integral equation , pure mathematics , biochemistry , chemistry , repressor , transcription factor , gene
We investigate solvability of a fractional analogue of the Neumann problem for the Laplace equation. As a boundary operator we consider operators of fractional differentiation in the Hadamard sense. The problem is solved by reduction to an integral Fredholm equation. A theorem on existence and uniqueness of the problem solution is proved.