PHYSICS AND MATHEMATICS

Solution of nonclassical integral Volterra equations of first kind with degenerate nonlinear kernel

A. A. Asanov^a, S. M. Choyubekov<sup>b

a</sup> Kyrgyz-Turkey Manas University
^b Osh State University

Abstract: Integral equations relate to the branch of mathematics, the important thing of which is that a large number of problems a wide range of sections of physics, engineering, and other sciences are reduced to them. Because of this, in recent years the theory of integral equations has been developing rapidly due to the work of many researchers.
However, equations with two variable limits of integration, which are called non-classical, have been little studied.
This is probably due to the difficulties in constructing of resolvent and in constructing a correlation for it since the analytical representation in general form has not yet been obtained except for some model cases.

Keywords: integral equation, Dirichlet formula, small parameter, double integrals.

DOI: 10.23670/IRJ.2018.70.029