Integral representations of solutions for a case of a model Volterra integral equation with a supersingular kernels
In the article, for a model integral equation, depending on the roots of the characteristic equation, general integral representations of solutions in terms of arbitrary constants are found. It follows from integral representations that for a model integral equation there are cases when a homogeneous integral equation can have non-zero solutions, that is, the theory of these integral equations differs significantly from the classical theory of Volterra integral equations. The conditions are found for the parameters of the integral equation, under which the inhomogeneous integral equation has a unique solution, that is, in this case, the theories of these integral equations coincide with the classical theory of Voltaire integral equations.