Fractional calculus operators of special functions? The result is well predictable!

In this survey, we point out on some few basic classical results, combined with author's ideas and developments, that show how one can do the task at once, in the rather general case: for both operators of generalized fractional calculus and generalized hypergeometric functions. Thus, great part of the results in the mentioned publications are well predicted and fall just as special cases of the discussed general scheme.