The next meeting of the Joint Seminar of Analysis, Geometry and Topology Department will be held on March 28, 2017 at 14:00 in Room 478 of IMI.

A talk on:

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

will be delivered by Prof. Virginia Kiryakova.

Everybody is invited.

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 rather particular, special functions. Practically, these are exercises to calculate improper integrals of products of different special functions. The list of such works is rather long and yet growing daily.
So, to illustrate our general approach proposed rather earlier but systematized recently (Kiryakova, 1994,...,2017), we limit ourselves to mention here only a few of them as 15 examples. Since there is a great variety of special functions, as well as of operators of fractional calculus, 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 talk, 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. In this way, the greater part of the results in the mentioned publications are well predicted and fall just as rather special cases of the discussed general scheme.
V. Kiryakova, Generalized Fractional Calculus and Applications. Longman & J. Wiley, 1994;
V. Kiryakova, Fractional calculus operators of special functions? - The result is well predictable! Chaos Solitons and Fractals (2017), DOI: 10.1016/j.chaos.2017.03.006, To appear