Certain novel estimates within fractional calculus theory on time scales

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.

Keywords

• pólya-szegö type inequality
• čebyšev inequality
• riemann-liouville fractional integral
• time scale