Abstract
In many papers, various questions for integral equations have been investigated. In this paper, we have chosen a regularization parameter for solving the linear Volterra integral equation of the first kind. The aim of the study is to construct a regularizing operator and choose a regularization parameter. In the study, we have applied the concept of a derivative with respect to an increasing function, the regularization method according to M.M. Lavrentiev, methods of functional analysis, methods of transformation of equations, methods of integral and differential equations. The parameter for regularization is selected. Regularizing operator according to M.M. Lavrentiev is constructed and a uniqueness theorem is proved. The proposed methods can be used to study integral, integral-differential equations such as the Volterra integral equation of the first kind, as well as in the qualitative study of some applied processes in the field of physics, ecology, medicine, and the theory of complex systems control. They can be used in the further development of the theory of Volterra integral equations of the first kind. And also, when solving specific applied problems leading to equations of the first kind.
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