A Variety of Nabla Hardy’s Type Inequality on Time Scales

Ahmed A. El-Deeb, Samer D. Makharesh, Sameh S. Askar and Jan Awrejcewicz
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Ahmed A. El-Deeb: Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City, Cairo 11884, Egypt
Samer D. Makharesh: Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City, Cairo 11884, Egypt
Sameh S. Askar: Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
Jan Awrejcewicz: Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, 1/15 Stefanowski St., 90-924 Lodz, Poland

Mathematics, 2022, vol. 10, issue 5, 1-17

Abstract: The primary goal of this research is to prove some new Hardy-type ?-conformable dynamic inequalities by employing product rule, integration by parts, chain rule and ( ? , a ) -nabla Hölder inequality on time scales. The inequalities proved here extend and generalize existing results in the literature. Further, in the case when ? = 1 , we obtain some well-known time scale inequalities due to Hardy inequalities. Many special cases of the proposed results are obtained and analyzed such as new conformable fractional h -sum inequalities, new conformable fractional q -sum inequalities and new classical conformable fractional integral inequalities.

Keywords: conformable derivative; time scales; Hardy’s inequality; ( ? , a )-nabla Hölder inequality on timescales (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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