The Solvability and Explicit Solutions of Singular Integral–Differential Equations with Reflection

This article deals with a classes of singular integral–differential equations with convolution kernel and reflection. By means of the theory of boundary value problems of analytic functions and the theory of Fourier analysis, such equations can be transformed into Riemann boundary value problems (i....

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Bibliographic Details
Published inAbstract and applied analysis Vol. 2024; pp. 1 - 7
Main Authors Nagdy, A. S., Hashem, KH. M., Ebrahim, H. E. H.
Format Journal Article
LanguageEnglish
Published New York Hindawi 16.05.2024
John Wiley & Sons, Inc
Hindawi Limited
Subjects
Analytic functions
Boundary value problems
Differential equations
Fourier analysis
Fourier transforms
Integral equations
Mathematical research
Egypt
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Summary:This article deals with a classes of singular integral–differential equations with convolution kernel and reflection. By means of the theory of boundary value problems of analytic functions and the theory of Fourier analysis, such equations can be transformed into Riemann boundary value problems (i.e., Riemann–Hilbert problems) with nodes and reflection. For such problems, we propose a novel method different from classical one, by which the explicit solutions and the conditions of solvability are obtained.
ISSN:1085-3375
1687-0409
DOI:10.1155/2024/5523649