Certain subclass of analytic and multivalent functions defined by using a certain fractional derivative operator

Making use of a certain operator of fractional derivative, a new subclass F (n;p;; ) of analytic and p-valent functions with neg- ative coefficients is introduced and studied here rather systematically. Coefficient estimates, a distortion theorem and radii of p-valently close- to-convexity, starlikeness and convexity are given. Finally several appli- cations involving an integral operator and a certain fractional calculus operator are also considered.