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In this paper, we study a pair of unified and extended fractional integral operator involving the multivariable  I -functions and general class of multivariable polynomials. Here, we use Mellin transforms to obtain our main results. Certain properties of these operators concerning to their Mellin-transforms have been investigated. On account of the general nature of the functions involved herein, a large number of known (may be new also) fractional integral operators involved simpler functions can be obtained. We will also quote the particular case of the multivariable  H -function.

Fractional calculus pertaining to multivariable I-function defined by Prathima