This article proposes a new approach based on quantum calculus framework employing novel classes of higher order strongly generalized Ψ \Psi -convex and quasi-convex functions. Certain pivotal inequalities of Simpson-type to estimate innovative variants under the q ˇ 1 , q ˇ 2 {\check{q}}_{1},{\check{q}}_{2} -integral and derivative scheme that provides a series of variants correlate with the special Raina’s functions. Meanwhile, a q ˇ 1 , q ˇ 2 {\check{q}}_{1},{\check{q}}_{2} -integral identity is presented, and new theorems with novel strategies are provided. As an application viewpoint, we tend to illustrate two-variable q ˇ 1 q ˇ 2 {\check{q}}_{1}{\check{q}}_{2} -integral identities and variants of Simpson-type in the sense of hypergeometric and Mittag–Leffler functions and prove the feasibility and relevance of the proposed approach. This approach is supposed to be reliable and versatile, opening up new avenues for the application of classical and quantum physics to real-world anomalies.

中文翻译：

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考虑广义Ψ-凸函数和应用的辛普森型不等式的两种变量形式的量子估计

本文提出了一种基于量子微积分框架的新方法，该方法采用高阶强广义 Ψ \Psi -凸函数和拟凸函数的新类。在 q ˇ 1 , q ˇ 2 {\check{q}}_{1},{\check{q}}_{2} - 积分和导数方案下估计辛普森型的某些关键不等式一系列变体与特殊的Raina 功能相关。同时，提出了 aq ˇ 1 , q ˇ 2 {\check{q}}_{1},{\check{q}}_{2} -积分恒等式，并提供了具有新颖策略的新定理。作为应用的观点，我们倾向于说明两个变量 q ˇ 1 q ˇ 2 {\check{q}}_{1}{\check{q}}_{2} -Simpson 类型的积分恒等式和变体超几何和 Mittag-Leffler 函数的意义，并证明了所提出方法的可行性和相关性。