Hadamard type inequalities via fractional calculus in the space of exp-convex functions and applications

Abstract

In this article, we study basic properties of exp-convex functions and establish the corresponding Hadamard type integral inequalities along with fractional operators. A comparative analysis between the exp-convexity and classic convexity is discussed. Furthermore, several related integral identities and estimation of upper bounds of inequalities involved with fractional operators are proved. In addition, some indispensable propositions associated with special means are allocated to illustrate the usefulness of our main results. Besides, Mittag-Leffler type convex functions with weaker convexity than exp-convexity are also presented.