A Solution to a Boundary-Value Problem for Integro-Differential Equations with Weakly Singular Kernels

A. T. Assanova, Sh. N. Nurmukanbet

2021

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DOI 10.3103/s1066369x21110013
Data confidence 70 medium
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Abstract

A linear boundary-value problem for a system of integro-differential equations with weakly singular kernels is considered. Questions of the unique solvability and the construction of algorithms for finding solution to the considered problem are studied. Conditions for the solvability of the boundary-value problem for a system of integro-differential equations with weakly singular kernels are established using the Dzhumabaev parametrization method based on splitting the interval and introducing additional parameters. Necessary and sufficient conditions for the solvability of the two-point problem for integro-differential equations with weakly singular kernels are obtained.