Some inequalities for partial derivatives on time scales

TL;DR

This paper develops new inequalities for functions on time scales, extending Opial-type inequalities to multiple variables and applying them to partial differential dynamic equations.

Contribution

It introduces weighted inequalities for function compositions on time scales and generalizes Opial-type inequalities to multiple variables with applications.

Findings

New weighted inequalities for functions on time scales

Generalized Opial-type inequalities in several variables

Applications to partial differential dynamic equations

Abstract

We first prove some weighted inequalities for compositions of functions on time scales which are in turn applied to establish some new dynamic Opial-type inequalities in several variables. Some generalizations and applications to partial differential dynamic equations are also considered.