Fractional Calculus and Confluent Hypergeometric Function Applied in the Study of Subclasses of Analytic Functions

Abstract

The study done for obtaining the original results of this paper involves the fractional integral of the confluent hypergeometric function and presents its new applications for introducing a certain subclass of analytic functions. Conditions for functions to belong to this class are determined and the class is investigated considering aspects regarding coefficient bounds as well as partial sums of these functions. Distortion properties of the functions belonging to the class are proved and radii estimates are established for starlikeness and convexity properties of the class.

Keywords

• analytic function
• fractional integral
• confluent hypergeometric function
• coefficient bounds
• partial sum
• radii of starlikeness and convexity