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

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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.

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Funding

This research is funded by the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan (grant no. AP09258829).

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Authors and Affiliations

  1. Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan

    A. T. Assanova & S. N. Nurmukanbet

  2. Al-Farabi Kazakh National University, Almaty, Kazakhstan

    A. T. Assanova & S. N. Nurmukanbet

Authors
  1. A. T. Assanova
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  2. S. N. Nurmukanbet
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Correspondence to A. T. Assanova or S. N. Nurmukanbet.

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(Submitted by T. K. Yuldashev)

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Assanova, A.T., Nurmukanbet, S.N. A Solvability of a Problem for a Fredholm Integro-Differential Equation with Weakly Singular Kernel. Lobachevskii J Math 43, 182–191 (2022). https://doi.org/10.1134/S1995080222040047

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  • DOI: https://doi.org/10.1134/S1995080222040047

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