Assembling classical and dynamic inequalities accumulated on calculus of time scales

Abstract

In this paper, we present an extension of dynamic Renyi’s inequality on time scales by using the time scale Riemann–Liouville type fractional integral. Furthermore, we find generalizations of the well–known Lyapunov’s inequality and Radon’s inequality on time scales by using the time scale Riemann–Liouville type fractional integrals. Our investigations unify and extend some continuous inequalities and their corresponding discrete analogues.

Keywords

• time scales
• fractional riemann–liouville integral
• renyi’s inequality
• lyapunov’s inequality
• radon’s inequality
• шкалы времени
• дробный интеграл римана-лиувилля
• неравенство реньи
• неравенство ляпунова
• неравенство радона