The authors consider the following generalization of the Mittag-Leffler function
introduced in 1971 by T. R. Prabkahar. In its turn, this function is a special case of the generalized Wright function. The authors prove several formulas for the Riemann-Liouville fractional integrals and derivatives of the function with a power weight. The main significance of these formulas is that the result is obtained also in terms of a generalized Mittag-Leffler function of such a type, with a power weight as well.