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 $int_{a}^{x}(t/x)^{mu}f(t)dt/t$ and the modified differentiation ${delta}+{mu}({delta}=xD,D=d/dx)$ with real $mu$, being taken n times. Conditions are given for such a Hadamard-type fractional integration operator to be bounded in the space $X^{p}_{c}$(a, b) of Lebesgue measurable functions f on $R_{+}=(0,{infty})$ such that for c${in}R=(-{infty}{infty})$, in particular in the space $L^{p}(0,{infty});(1{le}{le}{infty})$. The existence almost every where is established for the coorresponding Hadamard-type fractional derivative for a function g(x) such that $x^{p}$g(x) have $delta$ derivatives up to order n-1 on [a, b] and ${delta}^{n-1}[x^{mu}$g(x)] is absolutely continuous on [a, b]. Semigroup and reciprocal properties for the above operators are proved.