This paper aims to obtain the bounds of a class of integral operators containing Mittag–Leffler functions in their kernels. A recently defined unified Mittag–Leffler function plays a vital role in connecting the results of this paper with the well-known bounds of fractional integral operators published in the recent past. The symmetry of a function about a line is a fascinating property that plays an important role in mathematical inequalities. A variant of the Hermite–Hadamard inequality is established using the closely symmetric property for $(\alpha ,m)$-convex functions.

In this article, we have established the Hadamard inequalities for strongly convex functions using generalized Riemann–Liouville fractional integrals. The findings of this paper provide refinements of some fractional integral inequalities. Furthermore, the error bounds of these inequalities are given by using two generalized integral identities.

Symmetry is a fascinating property of numerous mathematical notions. In mathematical analysis a function $f:[a,b]\to \mathbf{R}$ symmetric about $\frac{a+b}{2}$ satisfies the equation $f(a+b-x)=f\left(x\right)$. In this paper, we investigate the relationship of unified Mittag–Leffler function with some known special functions. We have obtained some integral transforms of unified Mittag–Leffler function in terms of Wright generalized function. We also established a recurrence relation along with another important result. Furthermore, we give formulas of Riemann–Liouville fractional integrals and fractional integrals containing unified Mittag–Leffler function for symmetric functions.

In the literature of mathematical inequalities, convex functions of different kinds are used for the extension of classical Hadamard inequality. Fractional integral versions of the Hadamard inequality are also studied extensively by applying Riemann–Liouville fractional integrals. In this article, we define $(\alpha ,h-m)$-convex function with respect to a strictly monotone function that unifies several types of convexities defined in recent past. We establish fractional integral inequalities for this generalized convexity via Riemann–Liouville fractional integrals. The outcomes of this work contain compact formulas for fractional integral inequalities which generate results for different kinds of convex functions.

Fractional integral operators are useful tools for generalizing classical integral inequalities. Convex functions play very important role in the theory of mathematical inequalities. This paper aims to investigate the Hadamard type inequalities for a generalized class of functions namely strongly $(\alpha ,h-m)$-p-convex functions by using Riemann–Liouville fractional integrals. The results established in this paper give refinements of various well-known inequalities which have been published in the recent past.