Abstract:We aim to present some formulas for the Saigo hypergeometric fractional integral and differential operators involving the generalized Mathieu series S µ (r), which are expressed in terms of the Hadamard product of the generalized Mathieu series S µ (r) and the Fox-Wright function p Ψ q (z). Corresponding assertions for the classical Riemann-Liouville and Erdélyi-Kober fractional integral and differential operators are deduced. Further, it is emphasized that the results presented here, which are for a seemingly complicated series, can reveal their involved properties via the series of the two known functions.