Fractional Opial dynamic inequalities

Volume 22, Issue 4, pp 363--380 http://dx.doi.org/10.22436/jmcs.022.04.05

Publication Date: September 05, 2020 Submission Date: June 22, 2020 Revision Date: July 22, 2020 Accteptance Date: July 24, 2020

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Authors

A. G. Sayed - Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City 11884, Cairo, Egypt. S. H. Saker - Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt. A. M. Ahmed - Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City 11884, Cairo, Egypt. - Department of Mathematics, College of Science, Jouf University, Sakaka (2014), Kingdom of Saudi Arabia.

Abstract

In this paper, we will prove some new fractional dynamic inequalities on time scales of Opial's type. The results will be proved by employing the chain rule and Holder's inequality on fractional time scales. As a special case of our results, when \(\alpha =1\), we will obtain several well-known dynamic Opial inequalities on time scales.

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Keywords

• Opial's inequality
• Holder's inequality
• time scales
• conformable fractinonal calculus

MSC

•  26A15
•  26D10
•  26D15
•  39A13
•  34A40
•  34N05

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