Generalized Fractional Integral Operators Involving the H―‐Function and Their Applications to Special Functions

This article focuses on the study of fractional integral operators involving the ‐function. Two main theorems are established that present new fractional integral formulas associated with the ‐function. Moreover, several well‐known results related to various special functions can be derived as particular cases by assigning suitable parameter values to the general formulas. The proposed results encompass and extend the fractional integral operators previously investigated by Saxena and Kumbhat, Saigo, Erdélyi‐Kober, and Riemann‐Liouville, thereby providing a broader framework within the theory of fractional calculus and special functions. MSC2020 Classification: 26A33, 33B15, 33C05, 33C20, 44A10, 44A20.