Advanced Generalizations of Weighted Opial-Type Inequalities in the Framework of Time Scale Calculus

This work presents refined and generalized forms of weighted Opial-type inequalities within the framework of time scale calculus. The proofs rely on several algebraic techniques, together with Hölder’s inequality and Keller’s chain rule. These results extend the classical Opial-type inequalities by embedding them into the time scale setting, which unifies both continuous and discrete analyses. Consequently, various integral and discrete inequalities emerge as particular cases of our main results, thereby broadening the applicability of Opial-type inequalities to dynamic systems and discrete models.