This is a short survey of the role of Meijer’s G-function in the developments of the topics from the title, related to works of some Bulgarian mathematicians, and especially in author’s studies since 1974. It is inspired by her recent visit to the Groningen University in Holland, the place where Prof. Cornelis Simon Meijer has studied and worked, and where now, the Bulgarian traces in this topic of Dutch origin have been emphasized. Another good provocation is the increasing attention that some foreign authors have recently paid to the history, development and actual applications to practical problems, of the so-called Mellin-Barnes type integrals giving rise to the most useful definition of the G-function. This generalized hypergeometric function happens to provide: solutions to wide classes of singular differential equations of arbitrary order with variable coefficients and to Volterra type integral equations; kernel-functions for a variety of linear integral and integro-differential operators of applied analysis; as well as a unification scheme for the other special functions of mathematical physics.