Inventive dynamic inequalities of Pachpatte type on time scales and applications

In this article, we report a set of unique dynamic inequalities for different time scales that are based on delta-derivatives. These proposed inequalities prove to be useful tools for investigating both qualitative and quantitative facets of a class of time-scale dynamic equations, in addition to enhancing and extending several inequalities found in the literature. The introduced inequalities aid in a more thorough comprehension of the features of these equations, which involve an unknown function and its associated delta derivatives. The endpoint of this article includes numerical illustrations to emphasize the practical significance of the developed results.