Integral inequalities and the Mittag-Leffler function play a crucial role in many branches of mathematics and applications, including fractional calculus, mathematical physics, and engineering. In this paper, we introduced an extended generalized Mittag-Leffler function that involved several well-known Mittag-Leffler functions as a special case. We also introduced an associated generalized fractional integral to obtain some estimates for fractional integral inequalities of the Hermite-Hadamard and Hermite-Hadamard-Fejér types. This article offered several analytical tools that will be useful to anyone working in this field. To demonstrate the veracity of our findings, we offered a few numerical and graphical examples. A few applications of modified Bessel functions and unitarily invariant norm of matrices were also given.
