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The purpose of this study is to develop new iterative oscillation criteria for second‐order half‐linear advanced dynamic equations. These findings improve and extend recently established criteria for the same equation by several authors as well as encompass the existing classical criteria for associated ordinary dynamic equations. Some examples are given to show that the outcomes are accurate, practical, and adaptable. [ABSTRACT FROM AUTHOR]

In this article, we mainly generalize the results in the literature for a fractional q-difference equation. Our study considers a more comprehensive type of fractional p , q -difference system of nonlinear equations. By the Banach contraction mapping principle, we obtain a unique solution. By Krasnoselskii's fixed-point theorem, we prove the existence of solutions. In addition, finite stability has been established too. The main results in the literature have been proven to be a particular corollary of our work. [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]

In this study, we extended and improved the oscillation criteria previously established for second-order differential equations to even-order differential equations. Some examples are given to demonstrate the significance of the results accomplished. [ABSTRACT FROM AUTHOR]