On Novel Inequalities of Hardy Type Via Delta‐Conformable Calculus in the Time‐Scale Setting

ABSTRACT In this article, we establish a set of novel conformable dynamic inequalities of the Hardy type within the framework of time‐scale calculus. The analysis is carried out using several key mathematical tools, including Keller's version of the chain rule, the integration by parts formula, and the Hölder inequality adapted to conformable time scales. Our main objective is to unify and generalize various Hardy‐type inequalities across different settings. Specifically, we recover several well‐known Hardy inequalities for the case . Moreover, we derive new results in the continuous, discrete, and quantum settings as special cases of our general findings. These contributions offer a significant extension to the existing literature on dynamic inequalities and provide a versatile framework for further studies in both fractional and time‐scale analysis.