Quantum calculus (the calculus without limit) appeared for the first time in fluid mechanics, noncommutative geometry and combinatorics studies. Recently, it has been included into the field of geometric function theory to extend differential operators, integral operators, and classes of analytic functions, especially the classes that are generated by convolution product (Hadamard product). In this effort, we aim to introduce a quantum symmetric conformable differential operator (Q-SCDO). This operator generalized some well-know differential operators such as Sàlàgean differential operator. By employing the Q-SCDO, we present subclasses of analytic functions to study some of its geometric solutions of q-Painlevé differential equation (type III).

量子微积分（无极限微积分）在流体力学，非交换几何和组合学研究中首次出现。最近，它已被纳入几何函数理论领域，以扩展微分算子，积分算子和解析函数的类，尤其是由卷积积（Hadamard积）生成的类。在这项工作中，我们旨在引入量子对称适形微分算子（Q-SCDO）。该算子推广了一些众所周知的微分算子，例如Sàlàgean微分算子。通过使用Q-SCDO，我们提出了解析函数的子类来研究q- Painlevé微分方程（III型）的一些几何解。