The present paper is devoted to the study of the fractional calculus operators to obtain a number of key results for the generalized multiindex Bessel function involving Saigo hypergeometric fractional integral and differential operators in terms of generalized Wright function. Various particular cases and consequences of our main fractional-calculus results as classical Riemann-Liouville and Erde´lyi-Kober fractional integral and differential formulas are deduced.