FRACTIONAL DIFFERENTIATION OPERATION IN THE FOURIER BOUNDARY PROBLEMS

FRACTIONAL DIFFERENTIATION OPERATION IN THE FOURIER BOUNDARY PROBLEMS

We use the algebra of unbounded differentiation operators t acting on the ring of differentiable functions. The analytical representation of the fractional degree of the operator t is used to construct the resolvents of three boundary problems for the Fourier equation. Periodic solutions of limiting...

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Bibliographic Details
Main Authors: Petrichenko Mikhail, Musorina Tatiana
Format: Article
Language:English
Published: Peter the Great St.Petersburg Polytechnic University 2020-06-01
Series:St. Petersburg Polytechnical University Journal: Physics and Mathematics
Subjects:
differential equation
abel–liouville formula
ring of operators
inverse operator
carrier
distribution
Online Access:https://physmath.spbstu.ru/article/2020.48.04/
Description
Summary:We use the algebra of unbounded differentiation operators t acting on the ring of differentiable functions. The analytical representation of the fractional degree of the operator t is used to construct the resolvents of three boundary problems for the Fourier equation. Periodic solutions of limiting Fourier problems in the algebra of differentiation operators coincide with classical solutions. The extension t+, is a continuous spectrum of the Fourier transform and allows us to obtain exact solutions of three limit problems for a domain of any dimension d>1.
ISSN:2405-7223

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