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The aim of this study is to refine the known Riccati transformation technique to provide new oscillation criteria for solutions to second-order dynamic equations over time. It is important to note that the convergence or divergence of some improper integrals on time scales depends not only on the integration function but also on the integration time scale. Therefore, there has been a motivation to find new oscillation criteria that can be applicable regardless of whether ∫ ζ 0 ∞ Δ ξ a (ξ) is convergent or divergent, in contrast to what has been followed in most previous works in the literature. We have provided an example to illustrate the significance of the obtained results. [ABSTRACT FROM AUTHOR]

In this work, we deduce a new criterion that guarantees the oscillation of solutions to linear Sturm–Liouville delay noncanonical dynamic equations; these results emulate the criteria of the Hille and Ohriska types for canonical dynamic equations, and these results also solve an open problem in many works in the literature. Several examples are offered, demonstrating that the findings achieved are precise, practical, and adaptable. [ABSTRACT FROM AUTHOR]