Abstract
This article proposes a new approach based on quantum calculus framework employing novel classes of higher order strongly generalized psi-convex and quasi-convex functions. Certain pivotal inequalities of Simpson-type to estimate innovative variants under the (q) over cap (1) , (q) over cap (2)-integral and derivative scheme that provides a series of variants correlate with the special Raina's functions. Meanwhile, a (q) over cap (1) , (q) over cap (2)-integral identity is presented, and new theorems with novel strategies are provided. As an application viewpoint, we tend to illustrate two-variable (q) over cap (1) , (q) over cap (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.