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Approximative condition for the continuity of a fractional derivative

Authors:	L G Shakh

Institution:	(1) Institute of Mathematics, Academy of Sciences of the Ukraine, Kiev

Abstract:	For the spaceC of functions having a Marchaud continuous fractional derivative of order > 0 on the closed interval 0, 1] and for the function class $H_r \bar \varepsilon ] = \{ f:E_n (f) \leqslant \varepsilon _n ,n \in N,f^{(t)} (1) = 0,j = \overline {0,r} \}$ it is proved that $H_r \bar \varepsilon ] \subset C^\alpha$ if and only if $\sum\limits_{i = 1}^\infty {\varepsilon _i j^{2\alpha - 1}< \infty }$ .Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 12, pp. 1719–1722, December, 1992.

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