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

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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