The paper is devoted to the study of fractional integration and differentiation on a finite interval [a, b] of the real axis in the frame of Hadamard setting. The constructions under consideration generalize the modified integration

and the modified differentiation

with real

, being taken n times. Conditions are given for such a Hadamard-type fractional integration operator to be bounded in the space

(a, b) of Lebesgue measurable functions f on

such that for c

, in particular in the space

. The existence almost every where is established for the coorresponding Hadamard-type fractional derivative for a function g(x) such that

g(x) have

derivatives up to order n-1 on [a, b] and

g(x)] is absolutely continuous on [a, b]. Semigroup and reciprocal properties for the above operators are proved.