On some investigations of alpha-conformable Ostrowski–Trapezoid–Grüss dynamic inequalities on time scales

Abstract

Abstract We prove new Ostrowski-type α-conformable dynamic inequalities and its companion inequalities on time scales by using the integration-by-parts formula on time scales associated with two parameters for functions with bounded second delta derivatives. When α = 1 $\alpha =1$ , we obtain some well-known time-scale inequalities due to Ostrowski. As particular cases, we obtain new continuous and discrete inequalities.

Keywords

• Montgomery identity
• Ostrowski-type inequality
• Trapezoid-type inequality
• Grüss-type inequality
• Time scales