Riesz potential and its commutators in generalized weighted Morrey spaces defined on Carleson curves

In this paper we take up a characterization of weighted inequalities for Riesz potential and its commutators in generalized weighted Morrey spaces Mp,? ?(?) defined on Carleson curves ? with the class of weights Fp,q. We prove the boundedness of Riesz potential I?? and its commutator |b,I??| from the spaces, Mp?1?1(?)to the spaces p,?2?2M(?), where 0 < ? < 1,1 < p <1/?,1/p-1/q= ?,(?1,?2)are positive measurable functions, (?1,?2) ? p,q F(?) and b ? BMO(?).