In this paper, we derive a new lemma including third-order derivative of a function via fractional integrals. Using this lemma, we establish some new fractional estimates for Hermite-Hadamard type inequalities for convex functions. Several special cases are also discussed. Some applications to special means of real numbers are also discussed. The ideas and techniques used in this paper may stimulate future investigations regarding Hermite-Hadamard type of inequalities and its application in different areas.

Tbilisi Mathematical Journal, Vol. 8(2) (2015), pp. 103-113