By using contemporary theory of inequalities, this study is devoted to propose a number of refinements inequalities for the Hermite−Hadamard's type inequality and conclude explicit bounds for the trapezoid inequalities in terms of s-convex mappings, at most second derivative through the instrument of generalized fractional integral operator and a considerable amount of results for special means. The results of this study which are the generalization of those given in earlier works are obtained for functions f where | f' | and | f'' | (or | f' | q and | f'' | q for q ≥ 1) are s-convex hold by applying the Hölder inequality and the power mean inequality.