  In this paper, the generalized fractional integral operators of two
generalized Mittag-Leffler type functions are investigated. The special cases
of interest involve the generalized Fox--Wright function and the generalized
M-series and K-function. In the next Section 2 we first recall some generalized
fractional integral operators among the most widely used in fractional
calculus. Section 3 is devoted to the definitions of M-series and K-function
and their relations to special functions. In Sections 4 and 5, effective
fractional calculus of the generalized M-series and the K-function is carried
out. The last section briefly concludes and opens up new perspectives. The
results established herein generalize recent properties of generalized
Mittag-Leffler type functions using left-and right-sided generalized fractional
differintegral operators. The note results also in important applications in
physics and mathematical engineering.
