On Bounds of fractional integral operators containing Mittag-Leffler functions for generalized exponentially convex functions

Abstract

Recently, a generalization of convex function called exponentially $ (\alpha, h-m) $-convex function has been introduced. This generalization of convexity is used to obtain upper bounds of fractional integral operators involving Mittag-Leffler (ML) functions. Moreover, the upper bounds of left and right integrals lead to their boundedness and continuity. A modulus inequality is established for differentiable functions. The Hadamard type inequality is proved which shows upper and lower bounds of sum of left and right sided fractional integral operators.