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In this paper, we introduce the class of generalized strongly convex functions using Raina's function. We derive two new general auxiliary results involving first and second order (p,q)-differentiable functions and Raina's function. Essentially using these identities and the generalized strongly convexity property of the functions, we also found corresponding new generalized post-quantum analogues of Dragomir-Agarwal's inequalities. We discuss some special cases about generalized convex functions. To support our main results, we offer applications to special means, to hypergeometric functions, to Mittag-Leffler functions and also to (p,q)-differentiable functions of first and second order that are bounded in absolute value.