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In this work we suggestion new methods investigation the model Volterra type integral equation with logarithmic singularity, kernel which consisting from composition polynomial function with logarithmic singularity and function with singular point. The problem investigation this type integral equation at 2 reduce to problem investigate the Volterra type integral equation (1) for 2 the theory for which was constructed in [2]. In this work, we investigation integral equation (1) at 2 1. In this case, we investigate integral equation (1) reduction it’s to integral equation type [2] (I) and one the following integral equation [1] . (II)

journal of mathematics and system science

Integral Representation of the Manifold Solution for New Class of the Volterra Type Integral Equation with a Boundary Singularity in the Case, When Kernel Contain Logarithmic Singularity and its Power