Year: 2026
Type: article
Abstract: This article considers the nonlinear integral Volterra-Stieltjes equation of the third kind on a finite interval. To solve this equation, a regularizing operator is constructed and a uniqueness theorem is proven. The research uses the concept of a derivative with respect to an increasing function, the method of regularization according to M. M. Lavrent'ev in functional analysis, methods of transformation of equations, and methods of integral and differential equations. The proposed methods can be used to study integral and integro-differential equations of the Volterra-Stieltjes type of higher orders, as well as in the qualitative study of some applied processes in the fields of physics, ecology, medicine, and the theory of control of complex systems. They can be used in the further development of the theory of integral equations in classes of ill-posed problems, in the numerical solution of Volterra-Stieltjes integral equations of the third kind, and when solving specific applied problems that lead to equations of the third kind.
Source: Bulletin of Science and Practice
Author: N. Bedelova
Institution: Osh State University
Language: Russian
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W7164851893
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