Some new generalizations for exponentially (s, m)-preinvex functions considering generalized fractional integral operators

The generalized fractional integral has been one of the most useful operators for modelling non-local behaviors by fractional differential equations. It is considered, for several integral inequalities by introducing the concept of exponentially (s, m)-preinvexity. These variants derived via an extended Mittag-Leffler function based on boundedness, continuity and Hermite-Hadamard type inequalities. The consequences associated with fractional integral operators are more general and also present the results for convexity theory. Moreover, we point out that the variants are useful in solving the problems of science, engineering and technology where the Mittag-Leffler function occurs naturally.