Let denote the class of -valent functions, which have the form
and satisfy the condition
where , , , , and
where is the fractional derivative operator of order [see f.e. S. Owa, Fractional calculus, Proc. Workshop, Ross Priory, Univ. Strathclyde/Engl. 1984, Res. Notes Math. 138, 164-175 (1985; Zbl 0614.30014)].
In this paper some results concerning the radii of -valently close-to- convexity, starlikeness and convexity for the class are obtained. Also some classes preserving integral operator of the form
for the class are determined.