Use of fractional calculus to evaluate some improper integrals of special functions.

In this paper we point out on some author's ideas and developments, combined with few basic classical results, that show how one can do the task posed in the title at once, and in 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 publications mentioned in References (and many others not in this limited list) are well predicted and come just as very special cases of the discussed general scheme. [ABSTRACT FROM AUTHOR]