<abstract><p>In this paper, $ k $-fractional integral operators containing further extension of Mittag-Leffler function are defined firstly. Then, the first and second version of Hadamard and Fejér-Hadamard inequalities for generalized $ k $-fractional integrals are obtained. Finally, by using these generalized $ k $-fractional integrals containing Mittag-Leffler functions, results for $ p $-convex functions are obtained. The results for convex functions can be deduced by taking $ p = 1 $.</p></abstract>

In this paper, a new type of convex function called 𝑛-polynomial exponential type GA-convex functions is introduced. Some algebraic properties of these introduced functions are determined and the new Hermite-Hadamard type inequalities are proved for 𝑛 -polynomial exponential type convex functions.

In this paper we obtain the Hermite-Hadamard Inequality for M ϕ A-strongly convex function. Using this M ϕ A−strongly convex function we get some new theorems and corollaries.

In this article, generalized versions of the k -fractional Hadamard and Fejér-Hadamard inequalities are constructed. To obtain the generalized versions of these inequalities, k -fractional integral operators including the well-known Mittag-Leffler function are utilized. The class of ( p , h )-convex functions for Hadamard-type inequalities give the generalizations of results which have been proved in literature for p -convex, h -convex, and several functions deducible from these two classes.

The purpose of this article is to demonstrate new generalized k -fractional Hadamard and Fejér–Hadamard integral inequalities for α , h − m -convex functions. To prove these inequalities, k -fractional integral operators including the generalization of the Mittag–Leffler function are used. The results presented in this article can be considered an important advancement of previously published inequalities.