l-problem of moments for one-dimensional integro-differential equations with Erdélyi-Kober operators

Abstract

Purpose: to investigate the possibility of statement of l-problem of moments for one-dimensional linear equations of three types, which contain Erdélyi-Kober differential and integral operators of fractional order.
 Methods: formulation of l-problem of moments for each type of investigated equations, analytical investigation and solution of problem formulated
 Results. Conditions derived that determine the possibility and solvability of the problem stated. In some cases an explicit solutions of l-problem of moments obtained.
 Conclusions. The possibility of statement of formulated l-problem of moments shown in cases that defined by conditions obtained in paper. Some analytical solutions of investigated problem obtained.