**Authors:** V. I. Neaga, A. G. Scherbakova

### Abstract

The work defines the conditions of solvability of one system of integral convolutional equations with different degrees of differences in kernels. Such the system of the integral convolutional equations has not been studied earlier, and it turned out that all the methods used for the investigation of such a system with the help of Riemann boundary problem at the real axis can not be applied there. The investigation of such a type of the system of equations is based on the investigation of the equivalent system of singular integral equations with the Cauchy type kernels at the real axis. It is determined that the system of the equations is not a Noetherian one. Besides, we have shown the number of the linear independent solutions of the homogeneous system of equations and the number of conditions of solvability for the system of heterogeneous equations. The general form of these conditions is also shown and the spaces of solutions of that system of equations are determined. Thus the system of the convolutional equations that hasn't been studied earlier is presented in that work and the theory of its solvability is built here. So some new and interesting theoretical results are got in the paper.

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