A certain subclass of analytic functions involving operators of fractional calculus

Abstract

Making use of certain operators of fractional calculus, we introduce a new class T-mu(n,lambda,alpha) of functions which are analytic and univalent in the open unit disk U and obtain a necessary and sufficient condition for a function to be in the class T-mu(n,lambda,alpha). The various other results presented here for the class T-mu(n,lambda,alpha) include the radii of close-to-convexity, starlikeness, and convexity, end some growth and distortion theorems involving fractional integrals and fractional derivatives. Some interesting consequences and possible further generalizations of these results are also pointed out.