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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  L p   spaces. These inequalities are generally sharp in casep  &gt;  1    $p&amp;gt;1$    and best possible in casep  =  1    $p=1$   . Applications for the Hadamard fractional integrals are given.

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