Weighted Montgomery identity for the fractional integral of a function with respect to another function

Abstract

Abstract. We present a weighted Montgomery identity for the fractional integral of a function f with respect to another function g and use it to obtain weighted Ostrowski type inequalities for fractional integrals involving functions whose first derivatives belong to Lp spaces. These inequalities are generally sharp in case p > 1 $p>1$ and best possible in case p = 1 $p=1$ . Applications for the Hadamard fractional integrals are given.