On Some Hermite-Hadamard Type Inequalities for Convex Functions via Hadamard Fractional Integrals

The well-known Hermite-Hadamard integral inequality was established by Hermite at the end of 19th century (see [1]). There are many recent contributions to improve this inequality, please refer to [2,3,4,5,6] and references therein. It is worth noting that there are some interesting results about Hermite-Hadamard inequalities via fractional integrals according to the corresponding integral equalities involving a given class of differential convex functions. For more details on such new, important and interesting mathematical branch, one can refer to papers [7,8,9,10,11,12,13,14]. For a well defined convex function g on [c,d], the left (right) Hadamard fractional integral of order v > 0 is defined by (see [15]) (HJ v c+g)(z) = 1 Γ (v) ∫ z