Some subclasses of analytic functions associated with fractional calculus operators

Abstract

This paper begins by studying several properties and characteristics of certain subclasses of analytic functions with positive coefficients. The results investigated here include various coefficient inequalities, distortion properties, and the radii of close-to-convexity. Inclusion theorems involving the Hardy space of analytic functions and the class of functions whose derivative has a positive real part are also investigated. Relationships between certain subclasses of analytic functions (involving fractional derivative operators) with negative coefficients and a certain generalized fractional integral operator are then studied. Various known or new special cases of our results are also pointed out.