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A unified approach to certain fractional integration operators. (English) Zbl 0894.26002
In order to unify and extend the results on various fractional integration operators defined and studied during the last three decades, the authors investigate in this paper a pair of new fractional integral operators associated with multivariable $H$-function due to {\it H. M. Srivastava} and {\it R. Panda} [J. Reine Angew. Math. 283/284, 265-274 (1976; Zbl 0318.33006)] and a general class of polynomials introduced by {\it H. M. Srivastava} [Indian J. Math. 14, 1-6 (1972; Zbl 0249.33006)]. Some properties of these operators related to their Mellin transforms are investigated, generalizing the scores of results on various fractional integration operators scattered in the literature.

26A33Fractional derivatives and integrals (real functions)
33C70Other hypergeometric functions and integrals in several variables