Some Multidimensional Fractional Integral Operators Involving a General Class of Polynomials

In this paper the authors present a systematic investigation of two novel families of multidimensional fractional integral operators involving a general class of polynomials with essentially arbitrary coefficients. The various theorems established here involve compositions, inversion formulas, and multidimensional Mellin transforms, and convolutions of these general fractional integral operators. Each of the results obtained in this paper would unify and extend the corresponding (known or new) result for simpler families of fractional integral operators which were studied in several earlier works on the subject.