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In the present investigation, with the help of certain higher-order  q -derivatives, some new subclasses of multivalent  q -starlike functions which are associated with the Janowski functions are defined. Then, certain interesting results, for example, radius problems and the results related to distortion, are derived. We also derive a sufficient condition and certain coefficient inequalities for our defined function classes. Some known consequences related to this subject are also highlighted. Finally, the well-demonstrated fact about the    $(p,q)$  ( p , q ) -variations is also given in the concluding section.

Higher-order q-derivatives and their applications to subclasses of multivalent Janowski type q-starlike functions