Some new Hardy-type inequalities on time scales

Advances in Difference Equations

article

El-Deeb, Ahmed A.¹  Elsennary, Hamza A.¹  Baleanu, Dumitru² 

[1] Department of Mathematics, Faculty of Science, Al-Azhar University;Department of Mathematics, Cankaya University;Institute of Space Science;Department of Medical Research, China Medical University Hospital, China Medical University

关键词: Hardy’s inequality;    Dynamic inequality;    Time scale;   

DOI  :  10.1186/s13662-020-02883-8

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

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 Hölder 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.

【 授权许可】

CC BY