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Singular Integral Equations of Convolution Type With Carleman Shift

Author

Listed:
  • A. S. Nagdy
  • KH. M. Hashem
  • H. E. H. Ebrahim

Abstract

This article discusses a few different types of singular integral equations of the convolution type with Carleman shift in class {0}. By using the theory of Fourier analysis, these equations under consideration are transformed into Riemann–Hilbert boundary value problems for analytic functions with shift and discontinuous coefficients. For such problems, we propose a method different from the classical ones, and we obtain the analytic solutions and the conditions of Noether solvability. MSC2010 Classification: 45E10, 45E05, 30E25

Suggested Citation

  • A. S. Nagdy & KH. M. Hashem & H. E. H. Ebrahim, 2025. "Singular Integral Equations of Convolution Type With Carleman Shift," Abstract and Applied Analysis, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:jnlaaa:v:2025:y:2025:i:1:n:2599043
    DOI: 10.1155/aaa/2599043
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    References listed on IDEAS

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    1. A. S. Nagdy & KH. M. Hashem & H. E. H. Ebrahim, 2024. "The Solvability and Explicit Solutions of Singular Integral–Differential Equations with Reflection," Abstract and Applied Analysis, John Wiley & Sons, vol. 2024(1).
    2. Li, Pingrun & Ren, Guangbin, 2016. "Some classes of equations of discrete type with harmonic singular operator and convolution," Applied Mathematics and Computation, Elsevier, vol. 284(C), pages 185-194.
    3. Li, Pingrun, 2017. "Generalized convolution-type singular integral equations," Applied Mathematics and Computation, Elsevier, vol. 311(C), pages 314-323.
    4. A. S. Nagdy & KH. M. Hashem & H. E. H. Ebrahim & Paul Eloe, 2024. "The Solvability and Explicit Solutions of Singular Integral–Differential Equations with Reflection," Abstract and Applied Analysis, Hindawi, vol. 2024, pages 1-7, May.
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