Conditions for existence of solutions of linear integrodifferential equations with delay with analytical functions

Previously, with the help of the power series method, the author obtained conditions for the algorithmization of problems of establishing the existence of solutions of certain types of linear integrodifferential equations with analytic functions. This article shows that the applied method can also be used for linear integrodifferential equations with a proportional delay of the argument. A review of the usage of the "algorithm" concept in various branches of mathematics was made.