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

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.

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ACKNOWLEDGMENTS

The authors are sincerely grateful to the reviewer for worthy advises and helpful remarks which helped to improve the results of this work significantly.

Funding

This research is funded by the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan (Grant No. AP 09258829).

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Correspondence to A. T. Assanova or Sh. N. Nurmukanbet.

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Russian Text © The Author(s), 2021, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2021, No. 11, pp. 3–15.

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Assanova, A.T., Nurmukanbet, S.N. A Solution to a Boundary-Value Problem for Integro-Differential Equations with Weakly Singular Kernels. Russ Math. 65, 1–13 (2021). https://doi.org/10.3103/S1066369X21110013

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  • DOI: https://doi.org/10.3103/S1066369X21110013

Keywords

  • integro-differential equation
  • linear boundary value problem
  • kernel with weak singularity
  • Dzhumabaev parameterization method
  • solvability