Studies on generalized fractional operators in complex domain

Abstract

In the geometric function theory much attention is paid to various fractional operators (differential and integrals) mapping the class of univalent functions and its subclasses into themselves. Recently these operators have applications in different fields such as mathematical physics and computer sciences. In this note we shall introduce a generalized fractional differential operator for the class of univalent functions by employing the Srivastava-Owa fractional differential operator in the unit disk. Geometric properties such as convexity are discussed. Topological properties such as boundedness and compactness are studied in different spaces. Furthermore, conditions are given for the generalized fractional integral operator to be bounded in Hardy space.