**UDC: 681.3.057 https://doi.org/10.62965/tnu. sns.2024.1.1**

**Rajabov N., Rajabova L.**

**Tajik National University**

In this paper, for the first time, an overridden system of Volterra-type integral equations with singular or super-singular kernels is considered. It is proved that, when certain conditions are met, the problem of finding a solution to an over determined Volterra type

system of integral equations reduces to the problem of finding a solution to one-dimensional Volterra-type integral equations with singular or super-singular kernels, the theory of which is developed in the works of the author of this article. Depending on the sign of the values of functions in the kernels of the system of Volterra type integral equations, found manifold solution consideration system integral equation.

**Key words:** over determined system integral equations, singular kernels, integral representation, manifold solution.

**Information about the authors**

**Rajabov Nusrat** – Tajik National University,

Academician, Doctor of Physics and Mathematics, Professor of the Departments of Mathematical Analysis and Theory of Functions.

**Address**: 734025, Dushanbe,Republic of Tajikistan, Rudaki Avenue, 17.

**Phone**: (+992) 907-75-51-25. **E-mail**: This email address is being protected from spambots. You need JavaScript enabled to view it..

**Rajabova Lutfiya Nusratovna**** – **Tajik National University,

Doctor of Physics, and Mathematics, Professor of the Departments of Mathematical Analysis and Theory.

**Address**: 734025, Dushanbe, Republic of Tajikistan, Rudaki Avenue, 17.

**Phone**: (+992) 907-75-51-25**. E-mail**: This email address is being protected from spambots. You need JavaScript enabled to view it..

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**Article received:** 02.11.2023

**Approved after review:** 04.12.2023

**Accepted for publication:** 15.01.2024