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In this article we introduced and studied some inclusion properties for new subclasses of multivalent analytic functions defined by using the <i>q</i>-derivative operator. With the aid of the Jackson <i>q</i>-derivative we defined two new operators that generalize many other previously studied operators, and help us to define two new subclasses of functions with several interesting properties studied in this paper. The methods used for the proof of our results are special tools of the differential subordination theory of one-variable functions.