Some Hermite–Hadamard type inequalities for the fractionalintegrals are established and these results have some relationship withthe obtained results of [11, 12]. 1. IntroductionThe usefulness of inequalities involving convex functions is realized from thevery beginning and is now widely acknowledged as one of the prime drivingforces behind the development of several modern branches of mathematics andhas been given considerable attention. One of the most famous inequalities forconvex functions is Hermite–Hadamard inequality, stated as [8]:Let f : I ⊂ R→ Rbe a convex function on the interval I of real numbersand a,b ∈ I with a < b. Then(1) f a+b2 ≤1b−aZ ba f(x)dx ≤f(a) +f(b)2.Both inequalities hold in the reversed direction for f to be concave.In recent years, numerous generalizations, extensions and variants of Her-mite–Hadamard inequality (1) were studied extensively by many researchersand appeared in a number of papers, see [8, 10, 11, 12, 13].Now, somenecessarydefinitions and mathematicalpreliminariesoffractionalcalculus theory are presented, which are used further in this paper.Definition 1 ([9]). Let f ∈ L