k-Fractional inequalities associated with a generalized convexity

Abstract

The aim of this paper is to present the bounds of $ k $-fractional integrals containing the Mittag-Leffler function. For establishing these bounds, a generalized convexity namely strongly exponentially $ (\alpha, h-m)-p $-convexity is utilized. The results of this article provide many new fractional inequalities for several types of fractional integrals and various kinds of convexities. Moreover, an identity is established which helps in proving a Hadamard type inequality.

Keywords

• convex function
• strongly exponentially $ (\alpha
• h-m)-p $-convex function
• mittag-leffler function
• generalized fractional integrals