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

Abstract

Recently many authors are spending lot of time and efforts to evaluate various operators of fractional order integration and differentiation and their generalizations of classes of, or particular, special functions. The list of such works is rather long and yet growing daily, so we limit ourselves to mention here only a few, just to illustrate our general approach. As special functions present indeed a great variety, and the operators of fractional calculus do as well, the mentioned job produces a huge flood of publications. Many of them use same formal and standard procedures, and besides, often the results sound not of practical use, with except to increase authors’ publication activities.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.