Certain novel estimates within fractional calculus theory on time scales

Jian-Mei Shen; Saima Rashid; Muhammad Aslam Noor; Rehana Ashraf; Yu-Ming Chu; Jian-Mei Shen; Saima Rashid; Muhammad Aslam Noor; Rehana Ashraf; Yu-Ming Chu

doi:10.3934/math.2020390

AIMS Mathematics

2020, Volume 5, Issue 6: 6073-6086. doi: 10.3934/math.2020390

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Research article

Certain novel estimates within fractional calculus theory on time scales

1.
School of Finance and Statistics, Hunan University, Changsha 410079, P. R. China
2.
Department of Mathematics, Government College University, Faisalabad 38000, Pakistan
3.
Department of Mathematics, COMSATS University Islamabad 44000, Pakistan
4.
Department of Mathematics, Lahore College Women University, Lahore 54660, Parkstan
5.
Department of Mathematics, Huzhou University, Huzhou 313000, P. R. China
6.
Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science & Technology, Changsha 410114, P. R. China

Received: 18 May 2020 Accepted: 15 July 2020 Published: 24 July 2020
MSC : 26D15, 26A33, 26E70

The key purpose of this study is to suggest a delta Riemann-Liouville (RL) fractional integral operators for deriving certain novel refinements of Pólya-Szegö and Čebyšev type inequalities on time scales. Some new Pólya-Szegö, Čebyšev and extended Čebyšev inequalities via delta-RL fractional integral operator on a time scale that captures some continuous and discrete analogues in the relative literature. New explicit bounds for unknown functions concerned are obtained due to the presented inequalities.
- Pólya-Szegö type inequality,
- Čebyšev inequality,
- Riemann-Liouville fractional integral,
- time scale
Citation: Jian-Mei Shen, Saima Rashid, Muhammad Aslam Noor, Rehana Ashraf, Yu-Ming Chu. Certain novel estimates within fractional calculus theory on time scales[J]. AIMS Mathematics, 2020, 5(6): 6073-6086. doi: 10.3934/math.2020390

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Abstract

The key purpose of this study is to suggest a delta Riemann-Liouville (RL) fractional integral operators for deriving certain novel refinements of Pólya-Szegö and Čebyšev type inequalities on time scales. Some new Pólya-Szegö, Čebyšev and extended Čebyšev inequalities via delta-RL fractional integral operator on a time scale that captures some continuous and discrete analogues in the relative literature. New explicit bounds for unknown functions concerned are obtained due to the presented inequalities.

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