INTEGRAL EQUATIONS

Authors

  • S.Kh. Kholikov Navoiy State University, Associate Professor of the Department of Mathematics
  • R.R. Hamroyev Asia International University, Master’s Student,

DOI:

https://doi.org/10.55640/

Keywords:

integral equation, Fredholm equation, Volterra equation, successive approximation method, resolvent, numerical methods.

Abstract

This article presents the fundamental concepts of the theory of integral equations, the classification of integral equations, and the main analytical and numerical methods for solving them. Methods for finding solutions to Fredholm- and Volterra-type integral equations are discussed, in particular, the successive approximation method, the resolvent kernel, and the degenerate kernel method. The presented results serve to highlight the practical applications of the theory of integral equations..

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References

1.Kantorovich L. V., Akilov G. P. Functional Analysis. Pergamon Press, 1982.1

2.Tricomi F. G. Integral Equations. Dover Publications, 1985.

3.Polyanin A. D., Manzhirov A. V. Handbook of Integral Equations. CRC Press, 2008.

4. Kh. Kh. Turdiev, M. O. Rajabova, S. X. Xolikov, B. T. Karamatov, Direct and inverse coefficient problems for a fractional diffusion-wave equation with Riemann–Liouville derivative in time, Izvestiya Zavedeniy. Matematika, 2025, No. 11, https://doi.org/10.26907/0021-3446-2025-11-70-82

5.Maksudov Sh. T. Chiziqli integral tenglamalar elementlari. Toshkent, 1975.

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Published

2025-12-15

Issue

Vol. 4 No. 11 (2025): Journal of Multidisciplinary Sciences and Innovations

Section

Articles

License

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Authors retain the copyright of their manuscripts, and all Open Access articles are disseminated under the terms of the Creative Commons Attribution License 4.0 (CC-BY), which licenses unrestricted use, distribution, and reproduction in any medium, provided that the original work is appropriately cited. The use of general descriptive names, trade names, trademarks, and so forth in this publication, even if not specifically identified, does not imply that these names are not protected by the relevant laws and regulations.

How to Cite

INTEGRAL EQUATIONS. (2025). Journal of Multidisciplinary Sciences and Innovations, 4(11), 1939-1940. https://doi.org/10.55640/

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