On the approximation condition of continuity for the fractional derivative - Shakh , L. G. (Ukrains’kyi Matematychnyi Zhurnal, 1992)
For the space C^α of functions having a Marchaud continuous fractional derivative of order α>0 on the closed interval [0, 1] and for the function class H_r [ε ] = { f:E_n (f) ε _n ,n N,f^(i) (1) = 0, j = 0,r } it is proved that H_r [ε ]C^α if and only if _i = 1^∞ ε _i j^2α - 1< ∞ .