In this paper, we introduce and investigate two new subclasses of analytic functions in the open unit disk in the complex plane. Several interesting properties of the functions belonging to these classes are examined. Here, sufficient, and necessary and sufficient, conditions for the functions belonging to these classes, respectively, are also given. Furthermore, various properties like order of starlikeness and radius of convexity of the subclasses of these classes and radii of starlikeness and convexity of these subclasses are examined.