Newly, the hybrid fractional differential operator (HFDO) is presented and studied in Baleanu et al. (Mathematics 8.3:360, 2020). This work deals with the extension of HFDO to the complex domain and its generalization by using the quantum calculus. The outcome of the above conclusion is a q-HFDO, which will employ to introduce some classes of normalized analytic functions containing the well-known starlike and convex classes. Moreover, we utilize the quantum calculus to formulate the q-integral operator corresponding to q-HFDO. As a result, the upper solution is exemplified by utilizing the notion of subordination inequality.

中文翻译：

---

复域中量子混合分数阶可适微分和积分算子

最近，Baleanu 等人提出并研究了混合分数阶微分算子（HFDO）。（数学 8.3:360, 2020）。这项工作涉及 HFDO 到复杂域的扩展及其使用量子演算的泛化。上述结论的结果是一个 q-HFDO，它将用来引入一些包含众所周知的类星和凸类的归一化解析函数。此外，我们利用量子演算来制定对应于 q-HFDO 的 q-积分算子。因此，通过利用从属不等式的概念来举例说明上解。