On α-convex multivalent functions defined by generalized ruscheweyh derivatives involving fractional differential operator

Abstract

In the present investigation, we introduce a class of α-convex multivalent functions defined by generalized Ruscheweyh derivatives introduced by Goyal and Goyal (J. Indian Acad. Math. 27(2):439–456, 2005) which involves a generalized fractional differential operator. The necessary and sufficient condition for functions to belong to this class is obtained. We study properties of this class and derive a theorem about image of a function from this class through generalized Komatu integral operator. Also, the integral representation for the functions of this class has been obtained.