Some new Hardy-type inequalities on time scales

Abstract

In this paper, we will prove some new dynamic inequalities of Hardy-type on time scales. Some of the integral and difference inequalities that will be derived from our results in the continuous and discrete cases are original. The main results will be proved by using the dynamic Holder inequality, integration by parts formula on time scales, and Keller's chain rule on time scales. We will apply the main results to the continuous calculus, discrete calculus, and q-calculus as special cases.