A Solvability of a Problem for a Fredholm Integro-Differential Equation with Weakly Singular Kernel

Assanova A.T. Nurmukanbet S.N.
January 2022 Pleiades journals

Lobachevskii Journal of Mathematics
2022 #43 Issue 1 182 - 191 pp.

Abstract: Two-point boundary value problem for Fredholm integro-differential equation with singular kernel is considered. We propose a method for the investigation and solving of problem for the Fredholm integro-differential equation with weakly singular kernel based on the partition of the interval and introduction of additional parameters. Every partition of the interval is associated with a homogeneous Fredholm integral equation with weakly singular kernel of the second kind. The definition of regular partitions is presented. It is shown that the set of regular partitions is nonempty. A criterion for the solvability of the investigated problem is established and an algorithm for finding its solutions is constructed.

algorithm , Fredholm integral equations , Fredholm integro-differential equations , two-point boundary value problem , unique solvability , weakly singular kernel

Text of the article Перейти на текст статьи

Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Al-Farabi Kazakh National University, Almaty, Kazakhstan

Institute of Mathematics and Mathematical Modeling
Al-Farabi Kazakh National University

10 лет помогаем публиковать статьи Международный издатель

Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026