Kolmogorov type inequalities for the Marchaud fractional derivatives on   the real line and the half-line
  In this paper we establish some new Kolmogorov type inequalities for the Marchaud and Hadamard fractional derivatives of functions defined on a real axis or semi-axis. Simultaneously we solve two related problems: the Stechkin problem on the best approximation of unbounded operators by bounded ones on a given class of elements and the problem of optimal recovery of operator on elements from some class given with prescribed error. Keywords: inequalities for derivatives, fractional derivatives, approx- imation of unbounded operators by bounded ones, optimal recovery of operators, ideal lattice. 
V. F. Babenko, M. S. Churilova, N. V. Parfinovych, D. S. Skorokhodov
math.FA