This paper investigates some well-known inequalities for $q$- $h$-integrals. These include Hölder, Ostrowski, Grüss and Opial type inequalities. Refinement of the Hadamard inequality for $q$- $h$-integrals is also established by applying the definition of strongly convex functions. From main theorems, $q$-Hölder, $q$-Ostrowski and $q$-Grüss inequalities can be obtained in particular cases.

For generalizations of concepts of different fields fractional derivative operators as well as fractional integral operators are useful notions. Our aim in this paper is to discuss boundedness of the integral operators which contain Mittag-Leffler function in their kernels. The results are obtained for strongly $(\alpha ,h-m)$-convex functions which hold for different kinds of convex functions at the same time. They also give improvements/refinements of many already published results.