The core objective of this research is to introduce new classes of analytic functions by using the concept of bounded boundary rotation and some of its generalization. This research heavily depends on the recent techniques of convolution (Hadamard product) and the differential subordination. The Ruscheweyh derivative and Carlson-Shaffer operator are utilized to define certain new classes of analytic functions. We also investigate these classes for certain linear operators such as Jung-Kim-Srivastava operator, generalized Bernardi integral operator, Frasin integral operator and some others. Some geometrical and analytical properties, which include distortion bounds, radius problems, inclusion relation, rate of growth problem and integral representation, are explored systematically. Relevant connections of the results presented here with those obtained in earlier works are pointed out. This research is updated with the advancement and changing trends in the field of Geometric Function Theory and emerging new open problems are added for investigation.