Dynamic Hardy type inequalities via alpha-conformable derivatives on time scales

TL;DR

This paper establishes new Hardy-type inequalities involving alpha-conformable derivatives on time scales, unifying continuous, discrete, and quantum cases through dynamic calculus techniques.

Contribution

It introduces novel Hardy-type inequalities on time scales using alpha-conformable derivatives, extending classical results to a unified dynamic framework.

Findings

Derived new Hardy-type inequalities on time scales.

Unified continuous, discrete, and quantum inequalities as special cases.

Applied Keller's chain rule and integration by parts in the proofs.

Abstract

We prove new Hardy-type $\alpha$-conformable dynamic inequalities on time scales. Our results are proved by using Keller's chain rule, the integration by parts formula, and the dynamic H\"{o}lder inequality on time scales. When $\alpha=1$, then we obtain some well-known time-scale inequalities due to Hardy. As special cases, we obtain new continuous, discrete, and quantum inequalities.