A certain subclass of analytic functions associated with operators of fractional calculus

Abstract

In the present paper we introduce a new class of functions, defined by using certain fractional calculus operators, which are analytic in the open unit disk. A necessary and sufficient condition for a function to belong to such a class is obtained. The various other results presented here include the radii of close-to-convexity, starlikeness, and convexity, and some distortion theorems involving fractional integrals and fractional derivatives. Several special cases of our results are also pointed out.