System of nonlinear Volterra’s integral equations with polar kernel and singularities

We study an existence-uniqueness theorem for a system of nonlinear Volterra-type integral equations with polar kernel and singularities. To do so, we use a method of regularization of fractional derivatives with a delta sequence to avoid singularities over diagonal {y|x−y=0}{y|x−y=0}. The other singularities we regularize with delta sequences with different growth. As a framework, we use Colombeau special algebra.