Briot-Bouquet differential subordinations of analytic functions involving the Mittag-Leffler function defined in Cardioid domain

Abstract

In this researh work, we establish a new subclass of analytic functions constructed by the Mittag-Leffler function that maps the open unit disc onto the region bounded by the Cardioid domain. Using a technique introduced by Miller and Mocanu, we investigate several Briot-Bouquet differential subordinations for this function class.