The integral equation where 0<α<1, is considered under appropriate assumptions on K: For the approximate equation Au ≍ g regularization schemes are developed: (i) in Lp,(ii) in the space of functions of bounded variation, (iii) in the space of functions that are Holder continuous of order γ where 0 <γ<1. The extra information is in case in case ,in case (i) , in case (ii)Var , in case (iii) .