Volterra-Type Integro-Differential Equations with Two-Point Singular Differential Operator

First-order Volterra-type integro-differential equations with a two-point singular differential operator are considered. For this class of integro-differential equations, depending on the roots of the characteristic equation, integral representations of solutions are obtained. The case, when this equation has a unique solution, is studied. With the help of a two-point special differential operator, the integro-differential equation is replaced by corresponding operator-differential equation. In cases, when the roots of the corresponding characteristic equation are real different and complex conjugate, explicit solutions of the equation are constructed. Applying the results obtained for the model equation, the non-model equation is also investigated by the regularization method.