Error Estimates for Boole-Type Inequalities via Quantum Calculus with Their Numerical Analysis

This study presents new Boole-type integral inequalities for convex functions within the framework of quantum calculus. First, a quantum integral identity involving the left and right q-integral operators is established and subsequently used to derive several Boole-type inequalities under suitable convexity assumptions. Numerical examples, together with graphical representations, are provided to illustrate the theoretical results and to verify the derived bounds for different parameter values. This work broadens the understanding of quantum mechanics and mathematical inequalities, encouraging further research in this area.