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

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 Hölder 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.