Abstract
Research in this paper aims to explore the concept of generalized exponentially (s, m)-convex functions, and to determine some properties of these functions. In addition, we look at some interactions between generalized exponentially (s, m)-convex functions and local fractional integrals. The properties of the generalized new special cases of (s, m)-convex functions, s-convex functions, and also generalized m-convex functions are impressive. We derive some inequalities of Hadamard's type for generalized exponentially (s, m)-convex functions, and give applications in probability density functions and generalized special methods to attest to the applicability and efficiency of the method under consideration.